Appears in collection : 2025 - T1 - WS2 - Tempered representations and K-theory

Crossed product algebras are fundamental objects that describe actions of a Lie group G on a Fréchet algebra A. In this talk we will consider the convolution algebra of compactly supported smooth functions on G with values in A. Using geometrical arguments, we will canonically identify the periodic cyclic homology of this crossed product (up to a dimension shift) with the homology of the crossed product associated to a maximal compact subgroup. In this way we extend the results established by V. Nistor in the early 90' and provide a Mackey analogy in this framework.