Index theory for actions of compact Lie groups on C*-algebras

We study the index theory for actions of compact Lie groups on C*-algebras with an emphasis on principal actions. Given an invariant semifinite trace on the C*-algebra we obtain semifinite spectral triples. For circle actions we consider the relation to the dual Pimsner-Voiculescu sequence. On the way we show that the notions ``saturated'' and ``principal'' are equivalent for actions by compact Lie groups.