  We develop a theory of R-module Thom spectra for a commutative symmetric ring
spectrum R and we analyze their multiplicative properties. As an interesting
source of examples, we show that R-algebra Thom spectra associated to the
special unitary groups can be described in terms of quotient constructions on
R. We apply the general theory to obtain a description of the R-based
topological Hochschild homology associated to an R-algebra Thom spectrum.
