  We show that an operator valued $\alpha$-completely positive map on a group G
is given by a unitary representation of G on a Krein space which satisfies some
condition. Moreover, two unitary equivalent such unitary representations define
the same {\alpha}-completely positive map. Also we introduce a pre-order
relation on the collection of {\alpha}-completely positive maps on a group and
we characterize this relation in terms of the unitary representation associated
to each map.
