Nonabelian localization in equivariant K-theory and Riemann-Roch for quotients

الأصل · EN

We 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.