  We establish a localization theorem of Borel-Atiyah-Segal type for the
equivariant operational K-theory of Anderson and Payne. Inspired by the work of
Chang-Skjelbred and Goresky-Kottwitz-MacPherson, we establish a general form of
GKM theory in this setting, applicable to singular schemes with torus action.
Our results are deduced from those in the smooth case via Gillet-Kimura's
technique of cohomological descent for equivariant envelopes. As an
application, we extend Uma's description of the equivariant K-theory of smooth
compactifications of reductive groups to the equivariant operational K-theory
of all, possibly singular, projective group embeddings.
