  Let $\Oq(G)$ be the algebra of quantized functions on an algebraic group $G$
and $\Oq(B)$ its quotient algebra corresponding to a Borel subgroup $B$ of $G$.
We define the category of sheaves on the "quantum flag variety of $G$" to be
the $\Oq(B)$-equivariant $\Oq(G)$-modules and proves that this is a
proj-category. We construct a category of equivariant quantum
$\mathcal{D}$-modules on this quantized flag variety and prove the
Beilinson-Bernsteins localization theorem for this category in the case when
$q$ is not a root of unity.
