  We review the notions of a multiplier category and the $W^{*}$-envelope of a
$C^{*}$-category. We then consider the notion of an orthogonal sum of a
(possibly infinite) family of objects in a $C^{*}$-category. Furthermore, we
construct reduced crossed products of $C^{*}$-categories with groups. We
axiomatize the basic properties of the $K$-theory for $C^{*}$-categories in the
notion of a homological functor. We then study various rigidity properties of
homological functors in general, and special additional features of the
$K$-theory of $C^{*}$-categories. As an application we construct and study
interesting functors on the orbit category of a group from $C^{*}$-categorical
data.
