Twisted Deformation Quantization of Algebraic Varieties (Survey)
  Let X be a smooth algebraic variety over a field of characteristic 0. We introduce the notion of twisted associative (resp. Poisson) deformation of the structure sheaf O_X. These are stack-like versions of usual deformations. We prove that there is a twisted quantization map from twisted Poisson deformations to twisted associative deformations, which is canonical and bijective on equivalence classes. 
Amnon Yekutieli