  In this work we present a new definition to the Partial Crossed Product by
actions of inverse semigroups in a C^*-algebra, without using the covariant
representations as Sieben did in [5]. Also we present an isomorphism between
the partial crossed products by partial actions of a group G and the partial
crossed product by actions of S(G), an inverse semigroup associated to G
introduced by Exel in [2].
