  We give an operator algebraic model for the first group of the unit spectrum
$gl_1(KU)$ of complex topological K-theory, i.e. $[X, BGL_1(KU)]$, by bundles
of stabilized infinite Cuntz C*-algebras $O_{\infty} \otimes \K$. We develop
similar models for the localizations of $KU$ at a prime $p$ and away from $p$.
Our work is based on the $\mathcal{I}$-monoid model for the units of $K$-theory
by Sagave and Schlichtkrull and it was motivated by the goal of finding
connections between the infinite loop space structure of the classifying space
of the automorphism group of stabilized strongly self-absorbing C*-algebras
that arose in our generalization of the Dixmier-Douady theory and classical
spectra from algebraic topology.
