  In this paper, we examine the `derived completion' of the representation ring
of a pro-p group G_p^ with respect to an augmentation ideal. This completion is
no longer a ring: it is a spectrum with the structure of a module spectrum over
the Eilenberg-MacLane spectrum HZ, and can have higher homotopy information. In
order to explain the origin of some of these higher homotopy classes, we define
a deformation representation ring functor R[-] from groups to ring spectra, and
show that the map R[G_p^] --> R[G] becomes an equivalence after completion when
G is finitely generated nilpotent. As an application, we compute the derived
completion of the representation ring of the simplest nontrivial case, the
p-adic Heisenberg group.
