On the cohomology and the Chow ring of the classifying space of PGL_p
  We investigate the integral cohomology ring and the Chow ring of the classifying space of the complex projective linear group PGL_p, when p is an odd prime. In particular, we determine its additive structure completely, and we reduce the problem of determing its multiplicative structure to a problem in invariant theory. 
Angelo Vistoli