  This paper begins by noting that, in a 1969 paper in the Transactions,
M.C.McCord introduced a construction that can be interpreted as a model for the
categorical tensor product of a based space and a topological abelian group.
This can be adapted to Segal's very special Gamma--spaces, and then to a more
modern situation: (K tensor R) where K is a based space and R is a unital,
augmented, commutative, associative S--algebra.
  The model comes with an easy-to-describe filtration. If one lets K = S^n, and
then stabilize with respect to n, one gets a filtered model for the Topological
Andre--Quillen Homology of R. When R = Omega^{infty} Sigma^{infty} X, one
arrives at a filtered model for the connective cover of a spectrum X,
constructed from its 0th space.
  Another example comes by letting K be a finite complex, and R the S--dual of
a finite complex Z. Dualizing again, one arrives at G.Arone's model for the
Goodwillie tower of the functor sending Z to the suspension spectrum of
Map(K,Z).
  Applying cohomology with field coefficients, one gets various spectral
sequences for deloopings with known E_1--terms. A few nontrivial examples are
given.
  In an appendix, we describe the construction for unital, commutative,
associative S--algebras not necessarily augmented.
