  We give a Quillen equivalence between May and Sigurdsson's model category of
parametrized spectra over BG, and Mandell, May, Schwede, and Shipley's model
category of modules over the orthogonal ring spectrum \Sigma^\infty_+ G, for
each topological group G. More generally, for a topological category C we
introduce an "aggregate" model structure on the category of diagrams of spectra
indexed by C, and prove that it is Quillen equivalent to spectra over BC. This
lifts several earlier results, and leads to a complete characterization of the
dualizable parametrized spectra, answering a question of May and Sigurdsson.
