Corona algebras and strongly self-absorbing C^-dynamics

This article concerns the structure of C^{} -algebraic group actions induced on corona algebras from a given σ -unital C^{} -dynamical system over a locally compact group G . We prove that such actions satisfy the so-called dynamical folding property, which generalizes a fundamental property observed for corona algebras in works of Manuilov–Thomsen and Phillips–Weaver. We then focus on corona actions induced from G - C^{} -dynamics that are assumed to absorb a given strongly self-absorbing and unitarily regular G -action γ . It is proved that these corona actions are γ -saturated, which is a stronger property than being separably γ -stable. Conversely, if one assumes that the underlying C^{} -dynamics absorbs the trivial action on the compact operators, then γ -saturation of the corona action is equivalent to the original action being γ -absorbing. These results are a dynamical version of recent work by Farah and the third-named author.