  Let A be a \C-algebra with an action of a finite group G, let $\natural$ be a
2-cocycle on $G$ and consider the twisted crossed product $A \rtimes \C
[G,\natural]$. We determine the Hochschild homology of $A \rtimes \C
[G,\natural]$ 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 $A \rtimes \C [G,\natural]$. This paper prepares for a computation of the
Hochschild homology of the Hecke algebra of a reductive p-adic group.
