  We show that every interaction group extending an action of an Ore semigroup
by injective unital endomorphisms of a C*-algebra, admits a dilation to an
action of the corresponding enveloping group on another unital C*-algebra, of
which the former is a C*-subalgebra: the interaction group is obtained by
composing the action with a conditional expectation. The dilation is
essentially unique if a certain natural condition of minimality is imposed. If
the action is induced by covering maps on the spectrum, then the expectation is
faithful.
