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For a fixed prime p, we compute the Brown-Peterson cohomologies of classifying spaces of PU(p) and exceptional Lie groups by using the Adams spectral sequence. In particular, we see that BP*(BPU(p)) and K(n)*(BPU(p)) are even dimensionally generated.

The Brown-Peterson cohomology of the classifying spaces of the projective unitary groups 𝑃𝑈(𝑝) and exceptional Lie groups