In this paper a study of certain
conjugacy invariants of ergodic actions of countable discrete groups which appear in
the analysis of the associated group measure factors is begun. In particular a certain
maximal abelian subalgebra S of the factor associated to the free ergodic
measure-preserving action of a countable abelian group on a compact Lebesgue space
is studied. The structure of the normalizer of this subalgebra is completely
determined, and is shown to depend entirely on the point spectrum of the group
action. We examine cocycles of the group action with values in a compact abelian
group, the corresponding skew product actions and the related von Neumann
algebras. Conditions that such an extension be ergodic, and the point spectrum
distinct from the original action are obtained by examining the corresponding
factors. For actions with pure point spectrum we examine cocycles with values
in S1 and the corresponding ∗-automorphism of the factor and determine
necessary and sufficient conditions for the related Cartan subalgebra S to be
inner conjugate to its image under the cocycle automorphism. Applying our
results to a particular group action with pure point spectrum, we are able to
exhibit (modulo choice of an orbit equivalence) an uncountable family of
Cartan subalgebras in the hyperfinite II1 factor, no two of which are inner
conjugate.
