  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.
