Equivariant derived categories and descent theory for derived categories

I will talk about derived categories of equivariant sheaves on algebraic varieties. A series of examples of full exceptional collections in such categories will be presented, as well as general method to construct them. The construction starts from an exceptional collection in ordinary derived category and produces an exceptional collection in equivariant derived category by descent. In this context, I will give a simple but useful criterion for the derived category of a variety to be recovered from the derived category of its covering by means of descent.