  The paper presents a construction of the crossed product of a C*-algebra by a
commutative semigroup of bounded positive linear maps generated by partial
isometries. In particular, it generalizes Antonevich, Bakhtin, Lebedev's
crossed product by an endomorphism, and is related to Exel's interactions. One
of the main goals is the Isomorphism Theorem established in the case of actions
by endomorphisms.
