OnOK, I made a smooth manifoldreal hash of this the first time, so let me straighten this all out: Azumaya algebras (EDIT and a bundleat least as I understand them) are algebras which are locally isomorphic to $\mathrm{End}(E)$ for $E$ with projectively flat connection)a vector bundle. Note, you can compute the sheaf cohomology of any sheaf using its deRham complexI'm being a little vague here, since there are many contexts, many topologies, etc. Thuswhere one might want to do this. There's a general yoga for understanding such algebras: there's a coordinate atlas where they are trivial, ifso all you look atneed to say is the deRham differentialtrivialization on $\Omega(M,\mathrm{End}(E))$each patch, thenand what the cohomologytransition functions are. This is an element of Čech 1-cocycles for this cover for the global sections issheaf $H^n(M,\mathrm{End}(E))$. Since$\mathrm{End}(E)^*$; you can easily work out that the isomorphic Azumaya algebras are classified by elements ofthose that come from 2-cocyles via the boundary map $H^2(M,\mathrm{End}(E))$, they are classified(you conjugate the transitions by rankthe 2 differential forms which are closed-cocycle).
So, modulo those which are exactthe first sheaf homology of $\mathrm{End}(E)^*$ controls the Azumaya algebras; that's all I was trying to say; since it's a multiplicative sheaf, I think interpreting it as deRham cohomology will be trickier than I first imagined.