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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 thecategorical 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 moremodern 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, andthen stabilize with respect to n, one gets a filtered model for the TopologicalAndre--Quillen Homology of R. When R = Omega^{infty} Sigma^{infty} X, onearrives 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 ofa finite complex Z. Dualizing again, one arrives at G.Arone's model for theGoodwillie tower of the functor sending Z to the suspension spectrum ofMap(K,Z).  Applying cohomology with field coefficients, one gets various spectralsequences for deloopings with known E_1--terms. A few nontrivial examples aregiven.  In an appendix, we describe the construction for unital, commutative,associative S--algebras not necessarily augmented.

The McCord Model for the Tensor Product of a Space and a Commutative Ring Spectrum