The rational cohomology of a $p$-local compact group
By C. Broto, R. Levi, and B. Oliver

For any prime $p$, the theory of $p$-local compact groups is modelled on 
the $p$-local homotopy theory of classifying spaces of compact Lie groups 
and $p$-compact groups, and generalises the earlier concept of $p$-local 
finite groups. These objects have maximal tori and Weyl groups, although 
the Weyl groups need not be generated by pseudoreflections.  In this paper, 
we study the rational $p$-adic cohomology of the classifying space of a 
$p$-local compact group, and prove that just as for compact Lie groups, it 
is isomorphic to the ring of invariants of the Weyl group action on the 
cohomology of the classifying space of the maximal torus.