Noncommutative Poincare duality for boundary actions of hyperbolic groups

For a large class of word hyperbolic groups G the cross product C*-algebras C(partial derivativeGamma) X Gamma, where partial derivativeGamma denotes the Gromov boundary of Gamma satisfy Poincare duality in K-theory. This class strictly contains fundamental groups of compact, negatively curved manifolds. We discuss the general notion of Poincare duality for C*-algebras, construct the fundamental classes for the aforementioned algebras, and prove that KK-products with these classes induce inverse isomorphisms. The Baum-Connes Conjecture for amenable groupoids is used in a crucial way.