Higher Orbit Integrals, Cyclic Cocyles, and K-theory of Reduced Group C*-algebra

Abstract

Let G be a connected real reductive group. Orbit integrals define traces on the group algebra of G. We introduce a construction of higher orbit integrals in the direction of higher cyclic cocycles on the Harish-Chandra Schwartz algebra of G. We analyze these higher orbit integrals via Fourier transform by expressing them as integrals on the tempered dual of G. We obtain explicit formulas for the pairing between the higher orbit integrals and the K-theory of the reduced group C*-algebra, and discuss their applications to representation theory and K-theory.

arXiv comment41 pages, minor corrections

References in corpus (3)

• Geometric quantization for proper actions
• Parabolic induction and restriction via C*-algebras and Hilbert C*-modules
• Orbital integrals and $K$-theory classes

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• Higher orbital integrals, rho numbers and index theory
• Approximations of delocalized eta invariants by their finite analogues
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• An equivariant orbifold index for proper actions