A Fourier-Mukai Approach to the K-theory of Compact Lie Groups
  Let $G$ be a compact, connected, simply-connected Lie group. We use the Fourier-Mukai transform in twisted $K$-theory to give a new proof of the ring structure of the $K$-theory of $G$. 
David Baraglia and Pedram Hekmati
math.KT math.AT