# On the topological K-theory of twisted equivariant perfect complexes

## TL;DR

This paper establishes a comparison between topological K-theory of twisted perfect complexes on quotient stacks and twisted equivariant K-theory, proving their equivalence under certain conditions and providing new proofs for existing theorems.

## Contribution

It introduces a new comparison map and proves its equivalence in specific cases, extending previous work in twisted equivariant K-theory.

## Key findings

- Comparison map constructed and shown to be an equivalence under certain conditions
- New proof of Moulinos's theorem in the non-equivariant case
- Generalization of existing constructions in twisted K-theory

## Abstract

We construct a comparison map from the topological K-theory of the dg-category of twisted perfect complexes on certain global quotient stacks to twisted equivariant K-theory, generalizing constructions of Halpern-Leistner-Pomerleano and Moulinos. We prove that this map is an equivalence if a version of the projective bundle theorem holds for twisted equivariant K-theory. Along the way, we give a new proof of a theorem of Moulinos that the comparison map is an equivalence in the non-equivariant case.