2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72911We 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.27 pages; The proof of Lemma 4.4 is shorter; section 4.3 is new: now we can prove Prop. 2.3 without reference to Reisner's Thm. Other minor changes have been madeAlgebraic GeometryK-Theory and Homology14M25; 19E08text