  Using Kirchberg-Phillips' classification of purely infinite C*-algebras by
K-theory, we prove that the isomorphism types of crossed product C*-algebras
associated to certain hyperbolic 3-manifold groups acting on their Gromov
boundary only depend on the manifold's homology. As a result, we obtain
infinitely many pairwise non-isomorphic hyperbolic groups all of whose
associated crossed products are isomorphic. These isomomorphisms are not of
dynamical nature in the sense that they are not induced by isomorphisms of the
underlying groupoids.
