Title:Noncommutative Geometry and
Gamma-equivariant Characteristic Classes
Abstract: Consider an action of a discrete (pseudo) group G on a manifold M. Unless the action of G is free and proper, the quotient space M/G is practically meaningless when regarded as an ordinary space. To remedy this situation, A. Connes has proposed instead to replace it with the crossed-product algebra, which plays the role of the algebra of functions on the quotient. I will discuss constructions of characteristic classes in this context and their relationship to the index theory of such "quantum" quotient spaces.