Let W be a Coxeter group acting properly discontinuously and cocompactly on manifolds N and M (∂M = ∅) such that the fixed point sets of finite subgroups are contractible. Let f : (N, ∂N) → (M×Dk,M×Sk−1) be a W -homotopy equivalence which restricts to a W -homeomorphism on the boundary. Under an assumption on the three dimensional fixed point sets, we show that then f is W -homotopic to a W -homeomorphism.