In a [paper][1] from 1985, Raeburn and J. Taylor describe how to view all elements of H^2(X,Gm) (etale cohomology) as coming from non-unital Azumaya algebras. The construction relies on bimodule theory for these algebras.


  [1]: https://projecteuclid.org/journals/pacific-journal-of-mathematics/volume-119/issue-2/The-bigger-Brauer-group-and-%C3%A9tale-cohomology/pjm/1102706164.full