A Bott inverted model for equivariant unitary topological $K$-theory

Abstract

Let $\mathsf A$ be an abelian compact Lie group. We show the Bott inverted suspension spectrum of the projective space that classifies $\mathsf A$-equivariant line bundles is a model for $\mathsf A$-equivariant unitary topological $K$-theory.