Lets $X$ be a complex manifold (algebraic variety), $N$ an integer, and consider the sheaf $F$ defined by:

$F(U)$ ={ holomorphic maps $f: U\rightarrow GL(N,\mathbb{C})$ } with multiplicative structure.

Can we define $H^i(X,F)$ ? Note that for $N=1$, this would be just $H^i(X,O\_X^\*)$.

(Please give reference for your claims)