Partial generalized crossed products (expanded version).

Given a unital partial representation $\Theta $ of a group $G$ into the Picard semigroup ${\mathbf{PicS}}(R),$ we construct an abelian group ${\mathcal C}(\Theta /R) $ formed by the isomorphism classes of generalized partial crossed products related to $\Theta $ and identify an appropriate second partial cohomology group of $G$ with a naturally defined subgroup ${\mathcal C}_0(\Theta /R) $ of ${\mathcal C}(\Theta /R).$