  Let $\Gamma$ be a fuchsian subgroup of \pslr. In this paper we consider the
$\Gamma$-equivariant form of the Berezin's quantization of the upper half plane
which will correspond to a deformation quantization of the (singular) space
$\Bbb H/\Gamma$. Our main result is that the von Neumann algebra associated to
the $\Gamma-$ equivariant form of the quantization is stable isomorphic with
the von Neumann algebra associated to $\Gamma$.
