2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64900It is shown that all nontrivial elements in higher $K$-groups of toric varieties over a class of regular rings are annihilated by iterations of the natural Frobenius type endomorphisms. This is a higher analog of the triviality of vector bundles on affine toric varieties.final version, accepted for publication in Inventiones mathematicaeK-Theory and HomologyAlgebraic GeometryPrimary 14M25, 19D55; Secondary 19D25, 19E08text