  The Hochschild homology and cohomology group can be described in terms of the
homology and cohomology of the classifying space of the groupoid of the adjoint
action of the group under the suitable assumption of the finiteness of the
supports of cohomology groups. The difference between homology and cohomology
leads to a correction of the results in the book by D. J. Benson (1995),(1991).
