GEOFF BENNETT: The Ukrainian military is working with many international fighters in its battle against Russia, including Russian dissidents that have fled their homeland.

In May, a group of such fighters known as the Russian Volunteer Corps were part of a cross-border raid from Ukraine into Russia that made international headlines.

But the small group's white nationalist politics, including some neo-Nazi members, feeds into Vladimir Putin's false propaganda narrative that Ukraine is dominated by the far right.

We have this rare look at this group which was produced by videographer Ed Ram and special correspondent Jack Hewson, with support from the Pulitzer Center.

And a note: Names have been changed and faces blurred to protect the identity of some interviewees.

And some scenery was also blurred to help hide the location of where they filmed.

JACK HEWSON: Russian soldiers training on Ukrainian-held soil, an unusual sight, but these Russians have unusual aims.

ALEXANDER, Russian Volunteer Corps Fighter: Our ambitions are fairly simple, just destroy the current state in the Russian Federation.

JACK HEWSON: This is the Russia Volunteer Corps, or RVC, a far right revolutionary militia targeting Vladimir Putin.

VLADIMIR, Russian Volunteer Corps Fighter (through translator): Since my teenage years, I have always dreamt that something would change in the country where I was born and raised.

I wanted an armed fight against our criminal state to happen at some point.

JACK HEWSON: We were given rare access to the RVC and its leader, Denis Kapustin.

The group's far right white nationalist politics make it a controversial Ukrainian ally.

DENIS KAPUSTIN, Leader, Russian Volunteer Corps: Islamization, cultural Marxism, multiculturalism, I think all those -- all those things are harmful.

European culture is definitely endangered.

I believe in things like the Great Replacement.

JACK HEWSON: The RVC came to international attention in May with a daring incursion into the Russian Belgorod region.

It claimed to have seized this Russian armored personnel carrier, among other weaponry, and a number of prisoners of war, published in these RVC-branded videos that are posted to its Telegram channel.

They were pushed back to the border by Russian reinforcements within days, but have made sporadic raids since, embarrassing Russian forces by showing how easily its borders can be breached.

According to the RVC, their raids and attendant publicity have inspired many more to join the cause.

All these men here who are conducting target practice are Russian citizens who've come here to fight with the Ukrainians against Russia, and the only likelihood of them being able to go home to their motherland is if Ukraine wins and, in addition, they take territory inside Russia.

For new recruits like Alexander, it's a one-way ticket.

After what he claims to have done in Russia there's no going back.

ALEXANDER: Oh, I have committed several crimes within Russian border.

(LAUGHTER) ALEXANDER: You see, I have burned down several objects of infrastructure, and have made just some amount of explosive for further saboteurs.

JACK HEWSON: Potential recruits are encouraged to carry out sabotage to prove their worth.

Then, after entering Ukraine, they must be vetted by the Ukrainian intelligence services, including a lie-detector test, but one thing they appear not to be checking for is extreme political views.

ALEXANDER: As for my political views, I would describe them as just conservative.

There are guys who would say they are national socialists, anything of this sort.

I'm not.

I'm just conservative.

JACK HEWSON: Whether conservative or national socialist -- that's how the Nazis referred to themselves -- the RVC is known for harboring hard right extremists.

It is also led by one, Denis Kapustin, a former soccer hooligan and the owner of White Rex, a white nationalist mixed-martial arts and clothing brand using neo-Nazi symbolism connected to white supremacists and neo-Nazi groups across Europe and America.

DENIS KAPUSTIN: I spoke a lot with the guys who seem to share the same ideology as I do from United States, and they have some sort of a complete obsession with Jews, like Jews control everything.

I don't understand that thing.

I have -- I don't have a problem with actually any ethnicity.

JACK HEWSON: Whether antisemitic or not, he has a longstanding hostility towards migrants, particularly Muslims.

This is him speaking in 2017.

DENIS KAPUSTIN: Thirteen years ago, I was a just a common street gang skinhead, bashing immigrants in the street, setting their cars on fire, like breaking faces, whole program.

JACK HEWSON: Kapustin claims that he is not neo-Nazi, like at this press conference in June, where he said he would never be found making a Nazi salute.

Yet, at this White Rex MMA event from 2013, we see Denis in the white T-shirt cheering "Russians, go forward," with the crowd, some of whom are throwing Nazi salutes, which he then appears to mirror back.

The logic of Kapustin's politics is that Vladimir Putin is a multiculturalist and that the RVC represents true Russian white nationalism.

DENIS KAPUSTIN: I know a lot of nationalists all over the world think that, oh, Putin is a white power Christian leader of the white race, whatever.

And I said, guys, you have no idea what is going on in Russia.

I mean, Russia -- Moscow has the biggest Muslim population on the European continent.

JACK HEWSON: Whether or not you describe your politics as white nationalist or as neo-Nazi, many people watching this would think of that as being abhorrent.

Can you justify your position?

DENIS KAPUSTIN: I have said many times already in my interviews I might be a right-wing nationalist, conservative, or neo-Nazi, as you label me, OK, might be.

But I am right now fighting for democracy.

Right now, I'm fighting for your freedoms as well.

We might not be the good guys, but we're definitely fighting for the good cause.

JACK HEWSON: Whatever the RVC's politics, the Ukrainian military has welcomed its help.

But the alliance presents some uncomfortable questions.

Putin's propaganda line is that Russia is fighting neo-Nazis in Ukraine.

This is overwhelmingly untrue.

The vast majority of the forces fighting for Ukraine are not far right.

But the RVC's extreme politics lend some crumbs of truth to the Kremlin's propagandists, something we put to Ukrainian intelligence.

ANDRIY YUSOV, Main Intelligence Directorate (through translator): I think that, today, it's obvious to many people in the world that the main neo-Nazi and representative of authoritarian ideologies is Putin and his regime.

Many people from different countries are helping Ukrainians survive and fight against the Russian occupiers.

Although they might have different views, there are right-wing and left-wing, conservatives and liberals among them, but, when they are in Ukraine, they have to comply with Ukrainian laws, as well as the laws and principles of European democracy that Ukraine adheres to.

JACK HEWSON: But its on this point, abiding by democratic principles, that is questionable.

Kapustin shared with "PBS NewsHour" candid revelations on how the RVC dealt with a suspected Russian spy.

DENIS KAPUSTIN: We eliminated him.

JACK HEWSON: Tell me the story.

DENIS KAPUSTIN: One person tried to, let's say, set certain groups against each other and against me.

JACK HEWSON: Other than the fact that he was trying to overthrow you, what was the evidence that he was a spy?

DENIS KAPUSTIN: We obviously have our comrades in Russia who do different types of sabotage, infiltration, gather intel, things like that.

In his position, he was controlling that type of work.

And when we got our hands on his cell phones, we found that there was a lot of videos of guys sending, evidence of the work.

And he never forwarded those videos to us, but he forwarded those videos to some contact.

We didn't find out who that was, so that was more than suspicious.

JACK HEWSON: How did you kill him?

DENIS KAPUSTIN: Well, that would remain a secret.

But there was no -- no torture, no pain.

Let's put it like that.

JACK HEWSON: We asked the spokesman for Ukrainian intelligence, known as the GUR, about Kapustin's claims.

During our interview, Kapustin said that he had eliminated a suspected Russian spy from their ranks.

Was this ordered by the GUR?

ANDRIY YUSOV (through translator): I don't have information about this case.

But many factors should be taken into account, including where exactly on the territory of which state this happened and what the circumstances were.

JACK HEWSON: Are you concerned that there are potentially extrajudicial killings being carried out on Ukrainian soil under your watch?

ANDRIY YUSOV (through translator): Here, we're talking not about GUR, but about the Ukrainian security and defense sector in general.

Any such information must be carefully verified, and there must be an appropriate response from the state.

If detailed information about this is provided, of course we will send the materials for inspection.

JACK HEWSON: Ukraine is looking for all the help it can get in repelling the Russian invasion.

But partners like the RVC will continue to give them a P.R.

headache, especially if they operate outside the chain of command or breach of the Geneva Conventions.

For the "PBS NewsHour," I'm Jack Hewson in Ukraine.