### Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 10 (2014), 022, 26 pages      arXiv:1308.3871      https://doi.org/10.3842/SIGMA.2014.022

### The Real $K$-Theory of Compact Lie Groups

Chi-Kwong Fok
Department of Mathematics, Cornell University, Ithaca, NY 14853, USA

Received August 22, 2013, in final form March 06, 2014; Published online March 11, 2014

Abstract
Let $G$ be a compact, connected, and simply-connected Lie group, equipped with a Lie group involution $\sigma_G$ and viewed as a $G$-space with the conjugation action. In this paper, we present a description of the ring structure of the (equivariant) $KR$-theory of $(G, \sigma_G)$ by drawing on previous results on the module structure of the $KR$-theory and the ring structure of the equivariant $K$-theory.

Key words: $KR$-theory; compact Lie groups; Real representations; Real equivariant formality.

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