Let + be the positive cone of a totally ordered abelian discrete group , and an action of + by extendible endomorphisms of a C * -algebra A. We prove that the partial-isometric crossed product is a full corner of a group crossed product , where is a subalgebra of generated by a collection of faithful copies of A, and the action on is induced by shift on . We then use this realization to show that has an essential ideal J, which is a full corner in an ideal of .
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