We characterize the smooth toric varieties for which the Merkurjev spectral sequence, connecting equivariant and ordinary K-theory, degenerates. We find under which conditions on the support of the fan the $E^2$ terms of the spectral sequence are invariants by subdivisions of the fan. Assuming these conditions, we describe explicitly the $E^2$ terms, linking them to the reduced homology of the fan.
"Equivariant K-theory of smooth toric varieties." Tohoku Math. J. (2) 59 (2) 203 - 231, 2007. https://doi.org/10.2748/tmj/1182180734