  Let X be a nonsingular complex projective variety that is acted on by a
reductive group $G$ and such that $X^{ss} \neq X_{(0)}^{s}\neq \emptyset$. We
give formulae for the Hodge--Poincar\'e series of the quotient $X_{(0)}^s/G$.
We use these computations to obtain the corresponding formulae for the
Hodge--Poincar\'e polynomial of the moduli space of properly stable vector
bundles when the rank and the degree are not coprime. We compute explicitly the
case in which the rank equals 2 and the degree is even.
