2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73169We prove a localization formula in equivariant algebraic $K$-theory for an arbitrary complex algebraic group acting with finite stabilizer on a smooth algebraic space. This extends to non-diagonalizable groups the localization formulas H.A. Nielsen in equivariant $K$-theory of vector bundles and R.W. Thomason for higher $K$-theory of equivariant coherent sheaves. As an application we give a Riemann-Roch formula for quotients of smooth algebraic spaces by proper group actions. This formula extends previous work of B. Toen for stacks with quasi-projective moduli spaces and the authors for quotients by diagonalizable groups.To appear in Advances in Math (Artin volume); 38pages, latex.Minor revisions and deletions from previous versionAlgebraic GeometryK-Theory and Homologytext