Cohomology of classifying spaces and hermitian representations
George Lusztig
Department of Mathematics, Massachusetts Institute of Technology, 
Cambridge, Massachusetts 02139 
Represent. Theory 1 (1997), 31-36. 

Abstract. It is shown that a large part of the cohomology of the classifying 
space of a Lie group satisfying certain hypotheses can be obtained by a 
difference construction from hermitian representations of that Lie group. 
This result is relevant to the study of Novikov's higher signatures.