Bimodule deformations, Picard groups and contravariant connections

We study deformations of invertible bimodules and the behavior of Picard groups under deformation quantization. While K-0-groups are known to be stable under formal deformations of algebras, Picard groups may change drastically. We identify the semiclassical limit of bimodule deformations as contravariant connections and study the associated deformation quantization problem. Our main focus is on formal deformation quantization of Poisson manifolds by star products.