Cathelineau
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MR0369748 Cathelineau, Jean-Louis d?∞-cohomologie du classifiant d’un groupe complexe G à coefficients dans un G-module holomorphe. (French) C. R. Acad. Sci. Paris Sér. A 278 (1974), 1295?1298.
The author defines (p,q)-cohomology groups on the classifying space of a complex Lie group G with values in a holomorphic G-module and gives a spectral sequence formalism to compute them.
nLab page on d''-cohomology