2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/33379We 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.16pages, 1 figureDifferential GeometryK-Theory and Homologytext