Let X be a complete Riemannian manifold and let G be a discrete group acts on X freely, isometrically and cocompactly. It is known that the Atiyah L2-index of a G-invariant elliptic operator on X agrees with the Atiyah-Singer index of the corresponding elliptic operator on the base manifold X/G. However, when G acts properly instead of freely on X (so X/G is an compact orbifold), the L2-index does not agree with the Kawasaki's orbifold index for X/G. We study the difference of the two indices and present a K-theoretic index interpretation