Let $A$ be a C\*-algebra, $\alpha$ a strongly continuous automorphic action by a locally compact group $G$ on $A$, and consider the crossed product $A\rtimes\_\alpha G$. I am looking for references where I can read up on what is known about relations between the state spaces of $A$ and $A\rtimes\_\alpha G$. (The case $G={\mathbb R}^n$ would be sufficient for me.) 



States/functionals on crossed product C*-algebras
In the special case, where $A$ is the group vNa algebra of a type 1 group $H$, and $\alpha$ acts on $H$ via automorphism, then the extremal states on $A \rtimes\_\alpha G$ correspond roughly to irreducible representations of $H \rtimes\_\alpha G$ (assume that for instance that $H$ is compact), and these can be computed via the Mackey machine (Look at Mackey's paper "Group extensions of locally compact groups"). I would guess that Mark Rieffel has extended this to more general settings, but I am not very knowledgable in this area.


