  Let $\mathfrak{g}$ be a simple complex Lie algebra of a classical type and
$U_q(\mathfrak{g})$ the corresponding Drinfeld-Jimbo quantum group at $q$ not a
root of unity. With every point $t$ of the fixed maximal torus $T$ of an
algebraic group $G$ with Lie algebra $\mathfrak{g}$ we associate an additive
category $\mathcal{O}_q(t)$ of $U_q(\mathfrak{g})$-modules that is stable under
tensor product with finite-dimensional quasi-classical
$U_q(\mathfrak{g})$-modules. We prove that $\mathcal{O}_q(t)$ is essentially
semi-simple and use it to explicitly quantize equivariant vector bundles on the
conjugacy class of $t$.
