A short note on the continuous Rokhlin property and the universal coefficient theorem

Abstract: Let $G$ be a metrizable compact group, $A$ a separable C*-algebra and $\alpha$ a strongly continuous action of $G$ on $A$. Provided that $\alpha$ satisfies the continuous Rokhlin property, we show that the property of satisfying the UCT in E-theory passes from $A$ to the crossed product C*-algebra $A\rtimes_\alpha G$ and the fixed point algebra $A^\alpha$. This extends a result by Gardella in the case that $G$ is the circle and $A$ is nuclear. For circle actions on separable, unital C*-algebras with the continuous Rokhlin property, we establish a connection between the $E$-theory equivalence class of the coefficient algebra $A$ and the fixed point algebra $A^\alpha$.