2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61897We study the K-theory of actions of diagonalizable group schemes on noetherian regular separated algebraic spaces: our main result shows how to reconstruct the K-theory ring of such an action from the K-theory rings of the loci where the stabilizers have constant dimension. We apply this to the calculation of the equivariant K-theory of toric varieties, and give conditions under which the Merkurjev spectral sequence degenerates, so that the equivariant K-theory ring determines the ordinary K-theory ring. We also prove a very refined localization theorem for actions of this type.Addendum contains mainly a corrected definition of specialization maps, the previous one being wrong as noticed by A. Neeman. All the other results (in particular the main results) still hold. Several other typos also correctedAlgebraic GeometryK-Theory and Homology19E08; 14L30text