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

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 Toen [Théorèmes de Riemann-Roch pour les champs de Deligne-Mumford, K-Theory 18(1) (1999) 33-76] and the authors [Riemann-Roch for quotients and Todd classes of simplicial toric varieties, Comm. Algebra 31 (2003) 3735-3752].