The existence of quasimeromorphic mappings

Let G be a Kleinian group G acting on B-n, n >= 2. We show that if the orders of the elliptic elements in G which have non-degenerate fixed set are bounded, then G carries non-constant G-automorphic quasimeromorphic mappings. This together with an earlier non-existence theorem by Srebro gives a complete characterization of Kleinian groups that admit non-constant quasimeromorphic automorphic mappings.