  It is shown that the Euler characteristic
$\chi_{(\mathcal{H},\mathcal{B},\epsilon_q)}$ of a $\mathbb{Z}[[q]]$-Hecke
algebra $\mathcal{H}$ associated with a finitely generated Coxeter group
$(W,S)$ coincides with $p_{(W,S)}(q)^{-1}$, where $p_{(W,S)}(t)$ is the
Poincar\'e series of $(W,S)$.
