Note on C*-algebras associated to boundary actions of hyperbolic 3-manifold groups

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.
Comment: 11 pages; revision related to Theorem A: Bram Mesland and Haluk \c{S}eng\"un brought to our attention that a result analogous to Theorem A was obtained by them in the case of non-compact manifolds, using identical techniques (reference within the article)