On $K$-theory automorphisms related to bundles of finite order

TL;DR

This paper explores how finite order bundles influence the $K$-theory functor through classifying spaces, potentially enabling broader applications of twisted $K$-theory beyond traditional Picard group actions.

Contribution

It provides a new description of finite order bundle actions on $K$-theory using classifying spaces, expanding the framework for twisted $K$-theory.

Findings

Describes the action of finite order bundles on $K$-theory.

Suggests a new approach for general twistings in $K$-theory.

Potential for extending twisted $K$-theory beyond Picard group actions.

Abstract

In the present paper we describe the action of (not necessarily line) bundles of finite order on the $K$-functor in terms of classifying spaces. This description might provide with an approach for more general twistings in $K$-theory than ones related to the action of the Picard group.