Embeddings of Kleinian groups with torsion

Rips conjectured that a non-elementary word hyperbolic group is cohopfian i f and only if it is freely indecomposable. The results and examples in this paper show that cohopficity phenomenon in the case of word hyperbolic grou p with torsion is much more complicated than the conjecture. In particular, the cohopficity of such groups is not determined by the numbers of their e nds and the cohopficity is not preserved by finite index subgroups. Our res ults and examples arise from Kleinian groups. Orbifold structures and orbif old maps are the new tools in our discussions.