Given a C*-dynamical system (A, G,a), we discuss conditions under which sub
algebras of the multiplier algebra M(A) consisting of fixed points for alph
a are Morita-Rieffel equivalent to ideals in the crossed product of A by G.
In case G is abelian we also develop a spectral theory, giving a necessary
and sufficient condition for alpha to be equivalent to the dual action on
the cross-sectional C*-algebra of a Fell bundle. In our main application we
show that a proper action of an abelian group on a locally compact space i
s equivalent to a dual action. (C) 2000 Academic Press.