Part III, Free Actions of Compact Quantum Groups on $\mathrm{C}^*$-Algebras

We study and classify free actions of compact quantum groups on unital $\mathrm{C}^*$-algebras in terms of generalized factor systems. Moreover, we use these factor systems to show that all finite coverings of irrational rotation $\mathrm{C}^*$-algebras are cleft.