  In this paper, we study the extent to which Bousfield and finite
localizations relative to a thick subcategory of equivariant finite spectra
preserve various kinds of highly structured multiplications. Along the way, we
describe some basic, useful results for analyzing categories of acyclics in
equivariant spectra, and we show that Bousfield localization with respect to an
ordinary spectrum (viewed as an equivariant spectrum with trivial action)
always preserves equivariant commutative ring spectra.
