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We first want to consider the formal deformation of a fibered manifold $P\rightarrow M$ as a (bi-)module or subalgebra, where $M$ has a givendifferential star product. Consequently we want to find obstructions for theexistence of a bimodule or subalgebra, which turns out to be the curvature ofthe fiber bundle. Since the order by order construction of this structuresamounts to solving equations in the Hochschild cohomology of the smoothfunctions on $M$ with values in the differential operators on $P$, we proceedto computing this cohomology for the case of a smooth map $P \xrightarrow{p} M$such that $p(P)$ is a closed submanifold of $M$.

Bimodule deformation of fibered manifolds and the HKR theorem