  A Theorem due to Guillemin and Sternberg about geometric quantization of
Hamiltonian actions of compact Lie groups $G$ on compact Kaehler manifolds says
that the dimension of the $G$-invariant subspace is equal to the Riemann-Roch
number of the symplectically reduced space. Combined with the shifting-trick,
this gives explicit formulas for the multiplicities of the various irreducible
components. One of the assumptions of the Theorem is that the reduction is
regular, so that the reduced space is a smooth symplectic manifold. In this
paper, we prove a generalization of this result to the case where the reduced
space may have orbifold singularities. Our proof uses localization techniques
from equivariant cohomology, and relies in particular on recent work of
Jeffrey-Kirwan and Guillemin. Since there are no complex geometry arguments
involved, the result also extends to non Kaehlerian settings.
