G-theory of root stacks and equivariant K-theory

TL;DR

This paper explores the G-theory of root stacks using localization techniques and applies these findings to analyze the equivariant K-theory of algebraic varieties under specific conditions.

Contribution

It introduces a new approach to studying the G-theory of root stacks and connects it with equivariant K-theory of algebraic varieties.

Findings

G-theory of root stacks can be effectively studied via localization methods.

The results provide new insights into the equivariant K-theory of algebraic varieties.

Applications include understanding the K-theory under certain symmetry conditions.

Abstract

Using the description of the category of quasi-coherent sheaves on a root stack given in the paper of N. Borne and A. Vistoli, we study the G-theory of root stacks via localisation methods. We apply our results to the study of equivariant K-theory of algebraic varieties under certain conditions.