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We show that every interaction group extending an action of an Ore semigroupby injective unital endomorphisms of a C*-algebra, admits a dilation to anaction of the corresponding enveloping group on another unital C*-algebra, ofwhich the former is a C*-subalgebra: the interaction group is obtained bycomposing the action with a conditional expectation. The dilation isessentially unique if a certain natural condition of minimality is imposed. Ifthe action is induced by covering maps on the spectrum, then the expectation isfaithful.

Dilations of interaction groups that extend actions of Ore semigroups