Deformation quantization modules on complex symplectic manifolds

We study modules over the algebroid stack W-x of deformation quantization on a complex symplectic manifold x and recall some results: construction of an algebra for *-products, existence of (twisted) simple modules along smooth Lagrangian submanifolds, perversity of the complex of solutions for regular holonomic W-x-modules, finiteness and duality for the composition of "good" kernels. As a corollary, we get that the derived category of good W-x-modules with compact support is a Calabi-Yau category. We also give a conjectural Riemann-Roch type formula in this framework.