Partial generalized crossed products, Brauer groups and a comparison of seven-term exact sequences

Given a unital partial action α of a group G on a commutative ring R we study the abelian group C(Θ/R) of the isomorphism classes of partial generalized crossed products related to a unital partial representation Θ of G by isomorphism classes of partially invertible R-bimodules which are central over the α-invariants Rα. In particular, if Rα⊆R is an α-Galois extension, we show that the relative Brauer group B(R/Rα) is a quotient of C(Θ/R) by Pic(R). The results are applied to the partial action version of the Chase-Harrison-Rosenberg exact sequence.