Story highlights Putin accused of fuelling separatist rebellion in mainly Russian-speaking east of Ukraine

On international stage, Russia has been excluded from G8 group of industrialized nations

But Russian leader appears unmoved, his Ukraine policy unchanged

Putin told CNN's Matthew Chance: Russians should be given guarantees no one attacks us

The first frosts of winter have already dusted the spectacular city of St. Petersburg with a powder of glistening ice. The air outside feels sharp and crisp. Russians hurry along the elegant boulevards, wrapped up tight against the biting cold. Russia's winter, its annual deep freeze, has begun.

But this year there's more than just a bitter chill in the air. For the past nine months relations with the West have become decidedly frosty too.

On the face of it the problem is Ukraine.

The West backed a popular uprising there in March, which toppled a Kremlin-friendly government.

Infuriated, Russia's president, Vladimir Putin, annexed the strategic Crimean Peninsula, where it has a key naval base.

Since then he has been accused of fuelling a separatist rebellion in the mainly Russian-speaking east of the country. That unrest has already cost more than 4,000 lives.

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The United States and Europe have imposed costly sanctions and travel bans. It threatens more.

On the international stage, Russia has been excluded from the G8 group of industrialized nations. At the recent G20 summit in Brisbane, President Putin was cold-shouldered by his Western counterparts.

But the Russian leader appears unmoved, his Ukraine policy unchanged.

One fascinating explanation for the failure of Western sanctions and rebukes to change this vast country's behavior may be in the mindset, the world view, of its strongman president.

I'm one of the few Western journalists to have sat down with Vladimir Putin.

I asked him back then if he could guarantee that Russian troops would not invade other former Soviet states, like Ukraine.

He reacted quite angrily, saying he objected to my question. It was Russians, he said, who should be given guarantees that no one attacks us.

The comment sheds light, I think, on how Vladimir Putin sees the world outside the walls of the Kremlin.

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For him, Russia is under constant threat from the West. NATO expansion into former Eastern Bloc nations has eroded Russia's security. The prospect of Georgia joining the western military alliance, let alone Ukraine, is unthinkable for him.

The Cold War, from this perspective, has never really ended; we're still living in the 1980s.

The West, in particular the United States, still strives to "subjugate" Russia. President Putin repeated this just a few days ago in Moscow.

Sanctions are an inevitable consequence of Russia's resistance to this subjugation. Ukraine was the motive, but if it had not been Ukraine it would likely have been something else.

From a Western perspective, this seems like a cynical distortion of the facts, a Kremlin ploy to confuse and obfuscate.

But it may help explain why Russia is doing what it is doing, and why sanctions are not changing -- and may never change -- Kremlin policy.

It may also help to explain why, at a time of growing economic hardship, Russia's president remains so utterly popular at home.

His world view is theirs too. Like the harsh cold of the coming Russian winter, confrontation with the West is inevitable and must be endured.