A Riemann–Roch type theorem for twisted fibrations of moment graphs

Abstract

In the present paper we extend the Riemann–Roch formalism to structure algebras of moment graphs. We introduce and study the Chern character and push-forwards for twisted fibrations of moment graphs. We prove an analogue of the Riemann–Roch theorem for moment graphs. As an application, we obtain the Riemann–Roch type theorem for the equivariant $K$‑theory of some Kac–Moody flag varieties.