Hochschild homology of twisted crossed products and twisted graded Hecke algebras

Let A be a \C-algebra with an action of a finite group G, let $\mathrm{♮}$ be a 2-cocycle on $G$ and consider the twisted crossed product $A \rtimes \C [G,\natural]$\mathrm{.}WedeterminetheHochschildhomologyof$A \rtimes \C [G,\natural]$ for two classes of algebras A:

• rings of regular functions on nonsingular affine varieties,
• graded Hecke algebras. The results are achieved via algebraic families of (virtual) representations and include a description of the Hochschild homology as module over the centre of $A⋊\text{C}[G,\mathrm{♮}]$. This paper prepares for a computation of the Hochschild homology of the Hecke algebra of a reductive p-adic group.