Rigidity of Coxeter groups

Let W be a Coxeter group acting properly discontinuously and cocompactly on manifolds N and M (partial derivative M = ) such that the fixed point sets of finite subgroups are contractible. Let f : (N, partial derivative N) -- > (M x D-k, M x Sk-1) be a W-homotopy equivalence which restricts to a W-ho meomorphism on the boundary. Under an assumption on the three dimensional f ixed point sets, we show that then f is W-homotopic to a W-homeomorphism.