  Every hyperbolic group acts continuously on its Gromov boundary. One can form
the corresponding cross-product C*-algebra A. We show that there always exists
a canonical Poincare duality map from the K-theory of A to the K-homology of A.
We show that this map is an isomorphism when the group in question is the free
group on two generators. There is a direct connection between our constructions
and the Baum-Connes Conjecture, and we use the latter to deduce our result.
