The most interesting part of the G20 will be the meeting on the sidelines between President Obama and Dmitri Medvedev, his Russian counterpart. Russia is paying a lot of attention to the summit, and to the Nato gathering immediately afterwards. It’s had something of a triumph in the past year in shaping that alliance’s decisions without even being part of the club.

Russia is badly weakened by the financial crisis but its leaders are convinced that they hold a strong hand. Some of that is a delusion – certainly, if the oil price does not rise – but that will not stop them acting with confidence, more than US and European leaders may expect. There is plenty of room for misunderstanding, which could puncture the current mood of cooperation.

Since the turmoil hit hard in September, Medvedev and Vladimir Putin, the Prime Minister, have been less prickly towards Europe and the US. Analysts say that the Kremlin was shocked to run through a third of its foreign currency reserves in a few months, although the oil price is no longer plunging and markets appear to have accepted the level at which Russia wants to defend the rouble.

The Kremlin has become more civil, if not cordial, towards Western counterparts. Relations with Britain are a fraction better, helped by a meeting with Gordon Brown at the G8 summit last summer (which marked a decision on the British side to try to lift the chill). Putin and Medvedev said they welcomed Obama’s election as a chance for a change. This may reflect their recognition of economic vulnerability.

But it would be a mistake to think that they are approaching these summits in a conciliatory mood. Take last summer’s war with Georgia. Put bluntly, Russia won everything it wanted. It has kept its presence in Abkhazia and South Ossetia, Georgia’s breakaway provinces. It has undermined Mikheil Saakashvili, Georgia’s President, in the eyes of the White House and Georgians themselves. The question of Nato expansion (to Ukraine, Georgia and anywhere else) is now off the agenda (probably it always was, given German opposition, but that was not clear-cut a year ago).

The US team would be rash to assume requests for help on Iran or Afghanistan will be answered. The US offer not to put missile defences in Poland and the Czech Republic could easily be misinterpreted as a sign of weakness.

The huge shake-up of the army that Medvedev announced on Tuesday – focusing on the Caucasus and Central Asia, including Afghanistan’s borders – leaves Russia better placed to assert its influence against Nato’s. True, the new plan may be motivated by lack of cash but it shrewdly ditches the old obsession with pouring troops on to the Polish border, and shows an agile sense of how to maximise influence on a budget.

The economic turmoil has also strengthened Russia’s confidence in criticising the US. The G20 will provide a much better platform from which to proclaim the faults of Western capitalism than would the old G8, the club of rich nations. There, Russia holds its place on sufferance, having disappointed early predictions of its steady evolution towards democracy. In the G20, it will be backed up by the giants of the developing world if it lambasts the US for bringing misery to the world.

On the face of it, a financially weakened Russia should be easier to handle. But its leaders’ overriding confidence, based on the Georgian war and a belief that capitalism is in crisis, is a recipe for misunderstanding or even conflict.

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