Applications of model theory to C*-dynamics

As a third application we obtain the following result: if a C*-algebra A absorbs a strongly self-absorbing C*-algebra D, and α is an action of a compact group G on A with finite Rokhlin dimension with commuting towers, then α absorbs any strongly self-absorbing action of G on D. This has a number of interesting consequences, already in the case of the trivial action on D. For example, we deduce that D-stability passes from A to the crossed product. Additionally, in many cases of interest, our result restricts the possible values of the Rokhlin dimension to 0,1 and ∞, showing a striking parallel to the behavior of the nuclear dimension for simple C*-algebras. We also show that an action of a finite group with finite Rokhlin dimension with commuting towers automatically has the Rokhlin property if the algebra is UHF-absorbing.