Deformation quantization of complex involutive submanifolds

In this paper we start by defining what an algebroid stack is, and how it is locally described. We then discuss the algebroid stack of WKB operators on a complex symplectic manifold X and define the deformation quantization of an involutive submanifold V of X by means of simple WKB modules along V . Finally, we relate this deformation quantization to that given by WKB operators on the quotient of V by its bicharacteristic leaves.