  In 1990, Rieffel defined a notion of proper action of a group $H$ on a
$C^*$-algebra $A$. He then defined a generalized fixed point algebra
$A^{\alpha}$ for this action and showed that $A^{\alpha}$ is Morita equivalent
to an ideal of the reduced crossed product. We generalize Rieffel's notion to
define proper groupoid dynamical systems and show that the generalized fixed
point algebra for proper groupoid actions is Morita equivalent to a subalgebra
of the reduced crossed product. We give some nontrivial examples of proper
groupoid dynamical systems and show that if $(\A, G, \alpha)$ is a groupoid
dynamical system such that $G$ is principal and proper, then the action of $G$
on $\A$ is saturated, that is the generalized fixed point algebra in Morita
equivalent to the reduced crossed product.
