For a \(G\)-scheme \(X\) with a given equivariant perfect obstruction theory, we prove a virtual equivariant Grothendieck-Riemann-Roch formula, this is an extension of a result of \textit{B. Fantechi} and \textit{L. Göttsche} [Geom. Topol. 14, No. 1, 83--115 (2010; Zbl 1194.14017)] to the equivariant context. We also prove a virtual non-abelian localization theorem for schemes over \(\mathbb{C}\) with proper actions.

14C15, 14C40, 14L30, 19L47

Riemann-Roch theorems, equivariant Chow groups, equivariant \(K\)-theory

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Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany

Center for Geometry and Physics, Institute for Basic Science (IBS), Pohang 37673, Republic of Korea