# Enough vector bundles on orbispaces

## TL;DR

This paper proves that under mild conditions, orbispaces possess sufficient vector bundles, enabling their K-theory to be viewed as a cohomology theory and providing global presentation results for related geometric structures.

## Contribution

It establishes the existence of enough vector bundles on orbispaces and derives consequences for K-theory and global presentations of orbifold structures.

## Key findings

- Orbispaces with mild hypotheses have enough vector bundles.
- K-theory of these orbispaces forms a cohomology theory.
- Global presentation results for smooth and derived orbifolds are obtained.

## Abstract

We show that every orbispace satisfying certain mild hypotheses has 'enough' vector bundles. It follows that the K-theory of finite rank vector bundles on such orbispaces is a cohomology theory. Global presentation results for smooth orbifolds and derived smooth orbifolds also follow.