2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76565Mapping a locally free module to its l-th tensor power gives rise to a natural map from the Grothendieck group of all locally free modules to the Grothendieck group of all locally free representations of the l-th symmetric group. In this paper, we prove some formulas of Riemann-Roch type for the behaviour of this tensor power operation with respect to the push-forward homomorphism associated with a projective morphism between schemes. We furthermore establish analogous formulas for higher K-groups.42 pages, LaTex2eAlgebraic GeometryCommutative AlgebraK-Theory and HomologyRepresentation Theorytext