  In this paper we present a new characterization of free group actions (in
classical differential geometry), involving dynamical systems and
representations of the corresponding transformation groups. In fact, given a
dynamical system, we provide conditions including the existence of
"sufficiently many" representations of the transformation group which ensure
that the corresponding action of that group on the spectrum of the algebra is
free. In particular, the case of compact abelian groups is discussed very
carefully. We further present an application to the structure theory of
C*-algebras and an application to the noncommutative geometry of principal
bundles.
