  We analyze Parseval frames generated by the action of an
  ICC group on a Hilbert space. We parametrize the set of all such Parseval
frames by operators in the commutant of the corresponding representation. We
characterize when two such frames are strongly disjoint. We prove an
undersampling result showing that if the representation has a Parseval frame of
norm $\frac{1}{\sqrt{N}}$, the Hilbert space is spanned by an orthonormal basis
generated by a subgroup. As applications we obtain some sufficient conditions
under which a unitary representation admits a Parseval frame which is spanned
by an Riesz sequences generated by a subgroup. In particular, every
subrepresentation of the left regular representation of a free group has this
property.
