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Let P be a left LCM semigroup, and $\alpha$ an action of $P$ by endomorphismsof a $C^{*}$-algebra $A$. We study a semigroup crossed product $C^{*}$-algebrain which the action $\alpha$ is implemented by partial isometries. This crossedproduct gives a model for the Nica-Teoplitz algebras of product systems ofHilbert bimodules (associated with semigroup dynamical systems) studied firstby Fowler, for which we provide a structure theorem as it behaves well undershort exact sequences and tensor products.

Partial-isometric crossed products of dynamical systems by left LCM semigroups