This is part III (the last one) of the talk started on Feb 11:

http://pi.math.cornell.edu/m/node/10885

It will be self-contained and mostly independent of the previous parts.
I will give a brief overview of the theory of p-compact groups (p-local
homotopical analogs of compact Lie groups) and explain how to construct
some basic ``exotic'' examples: the Sullivan spheres and the Clark-Ewing spaces.
I will then define quasi-invariants for general (non-Coxeter) pseudo-reflection groups
and explain how these can be realized topologically in terms of classifying spaces
of p-compact groups.