  We compute the equivariant $K$-theory $K_G^*(G)$ for a simply connected Lie
group $G$ (acting on itself by conjugation). We prove that $K_G^*(G)$ is
isomorphic to the algebra of Grothendieck differentials on the representation
ring. We also study a special example of a non-simply connected Lie group $G$,
namely PSU(3), and compute the corresponding equivariant $K$-theory.
