  In general the processes of taking a homotopy inverse limit of a diagram of
spectra and smashing spectra with a fixed space do not commute. In this paper
we investigate under what additional assumptions these two processes do
commute. In fact we deal with an equivariant generalization which involves
spectra and smash products over the orbit category of a discrete group. Such a
situation naturally occurs if one studies the equivariant homology theory
associated to topological cyclic homology. The main theorem of this paper will
play a role in the generalization of the results obtained by Boekstedt, Hsiang
and Madsen about the algebraic K-theory Novikov Conjecture to the assembly map
for the family of virtually cyclic subgroups.
