  We prove structural theorems for computing the completion of a G-spectrum at
the augmentation ideal of the Burnside ring of a finite group G. First we show
that a G-spectrum can be replaced by a spectrum obtained by allowing only
isotropy groups of prime power order without changing the homotopy type of the
completion. We then show that this completion can be computed as a homotopy
colimit of completions of spectra obtained by further restricting isotropy to
one prime at a time, and that these completions can be computed in terms of
completion at a prime.
  As an application, we show that the spectrum of stable maps from BG to the
classifying space of a compact Lie group K splits non-equivariantly as a wedge
sum of p-completed suspension spectra of classifying spaces of certain
subquotients of the product of G and K. In particular this describes the dual
of BG.
