Attached to any reductive Lie group G is a “Cartan motion group” G_0 —a Lie group with the same dimension as G, but a simpler group structure. There exists a natural one-to-one correspondence between the irreducible tempered representations of G and the unitary irreducible representations of G_0 and a deformation procedure. In this talk, we will discuss the orbital integral of generators in K-theory of the group C*-algebra of G_0 and show they are independent of the deformation.

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