The official Chechen resistance has denounced the Chechens who have taken hostage a theater full of people in Moscow. This recognizes the fact that Chechens, as a whole, have not agreed on what to do with Chechen religious radicals who insist on invading neighboring areas to establish, by force, an Islamic Republic in the Caucasus. A related problem are the criminal gangs who were using Chechnya as a refuge, while they ran criminal enterprises in areas surrounding Chechnya. Dealing with both of these are what brought the Russian army back to Chechnya and until the majority of Chechens can agree to deal with the Islamic radicals and criminals, the Russians cannot afford to leave. The current hostage incident just confirms, to many Russians, that the Chechens are just a bunch of bloodthirsty gangsters and religious fanatics.
For the past few years, more Chechens have openly advocated what amounts to civil war among Chechens to reduce the influence of Islamic radicals and gangsters. It's generally recognized that this is the only way the Russians can be convinced to pull their troops out. But so far, the Islamic radicals and gangsters still have more guys with guns.