Part II, Free Actions of Compact Groups on C*-Algebras
Kay Schwieger, Stefan Wagner

TL;DR
This paper investigates a specific class of free actions of non-Abelian compact groups on unital C*-algebras, called cleft actions, providing a classification and linking them to classical principal bundles.
Contribution
It introduces and classifies cleft actions of non-Abelian groups on C*-algebras, connecting noncommutative vector bundles to classical bundle theory.
Findings
Cleft actions are characterized by trivial associated noncommutative vector bundles.
A complete classification theory for cleft actions is developed.
Relations between cleft actions and classical principal bundles are established.
Abstract
We study a simple subclass of free actions of non-Abelian groups on unital C*-algebras, namely cleft actions. These are characterized by the fact that the associated noncommutative vector bundles are trivial. In particular, we provide a complete classification theory for these actions and describe its relations to classical principal bundles.
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