Compact Lie group actions with continuous Rokhlin property

In this paper, we study continuous Rokhlin property of ${\mathrm{C}}^{\ast }$-dynamical systems using techniques of equivariant $\mathrm{K}\mathrm{K}$-theory and quantum group theory. In particular, we determine the $\mathrm{K}\mathrm{K}$-equivalence class and give a classification of Kirchberg $G$-algebras when the $G$ is a compact Lie group with Hodgkin condition.