  For any Coxeter group W, we define a filtration of H^*(W;ZW) by W-submodules
and then compute the associated graded terms. More generally, if U is a CW
complex on which W acts as a reflection group we compute the associated graded
terms for H_*(U) and, in the case where the action is proper and cocompact, for
H^*_c(U).
