  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.
