Absorption conjecture for crossed products by compact group actions

Let $G$ be a second-countable compact group, let $A$ be a separable unital $C^*$-algebra, and let $\alpha\colon G\to\operatorname{Aut}(A)$ be an action of $G$ on $A$ with finite Rokhlin dimension with commuting towers. Let $\mathcal{D}$ be a strongly self-absorbing $C^*$-algebra and suppose that $A$ is $\mathcal{D}$-absorbing. Absorption conjecture. Then $A\rtimes_\alpha G$ is $\mathcal{D}$-absorbing. The conjecture generalizes the paper's preservation results for Jiang–Su absorption under compact group actions. Its status is not resolved in the supplied text.