@article{Hochs2018OrbitalIA,
title={Orbital integrals and \$K\$-theory classes},
author={P. Hochs and Hang Wang},
journal={arXiv: K-Theory and Homology},
year={2018}
}

Let $G$ be a semisimple Lie group with discrete series. We use maps $K_0(C^*_rG)\to \mathbb{C}$ defined by orbital integrals to recover group theoretic information about $G$, including information contained in $K$-theory classes not associated to the discrete series. An important tool is a fixed point formula for equivariant indices obtained by the authors in an earlier paper. Applications include a tool to distinguish classes in $K_0(C^*_rG)$, the (known) injectivity of Dirac inductionâ€¦Â CONTINUE READING