The Euler characteristic of a Hecke algebra

It is shown that the Euler characteristic χ(H,B,εq)χ(H,B,εq) of a Z〚q〛Z〚q〛-Hecke algebra HH associated with a finitely generated Coxeter group (W,S)(W,S) coincides with p(W,S)(q)−1p(W,S)(q)−1, where p(W,S)(t)p(W,S)(t) is the Poincaré series of (W,S)(W,S).