  In this paper we complete the proof of Caldararu's conjecture on the
compatibility between the module structures on differential forms over
poly-vector fields and on Hochschild homology over Hochschild cohomology. In
fact we show that twisting with the square root of the Todd class gives an
isomorphism of precalculi between these pairs of objects.
  Our methods use formal geometry to globalize the local formality
quasi-isomorphisms introduced by Kontsevich and Shoikhet (the existence of the
latter was conjectured by Tsygan). We also rely on the fact - recently proved
by the first two authors - that Shoikhet's quasi-isomorphism is compatible with
cap product after twisting with a Maurer-Cartan element.
