K-Theory of Group C* Algebras (An Introduction to K-Theory and the Baum-Connes Conjecture)

A SpinC-manifold is a C\infty manifold with a given structure which is slightly stronger than an orientation. A Spin C manifold has a Dirac operator. This is a first order elliptic differential operator. The (equivariant) indices of these Dirac operators can be used to formulate BC for discrete groups.