Global Homotopies for Differential Hochschild Cohomologies

We construct global homotopies to compute differential Hochschild cohomologies in differential geometry. This relies on two different techniques: a symbol calculus from differential geometry and a coalgebraic version of the van Est theorem. Not only do we obtain an improved version of the Hochschild-Kostant-Rosenberg theorem but we also compute Hochschild cohomologies for related scenarios, e.g. for principal bundles, and invariant versions.