  The wreath product W(r,n) of the cyclic group of order r and the symmetric
group S_n acts on the corresponding projective hyperplane complement, and on
its wonderful compactification as defined by De Concini and Procesi. We give a
formula for the characters of the representations of W(r,n) on the cohomology
groups of this compactification, extending the result of Ginzburg and Kapranov
in the r=1 case. As a corollary, we get a formula for the Betti numbers which
generalizes the result of Yuzvinsky in the r=2 case. Our method involves
applying to the nested-set stratification a generalization of Joyal's theory of
tensor species, which includes a link between polynomial functors and plethysm
for general r. We also give a new proof of Lehrer's formula for the
representations of W(r,n) on the cohomology groups of the hyperplane
complement.
