In this paper I show that there is an integral version of elliptic
homology which is a tensored down version of Spin bordism. That is,
there is a theory El such that El(X) is MSpin(X) tensor over MSpin of a
point with El of a point. If you invert 2, El gives the usual
Landweber-Ravenel-Stong elliptic homology. The theory El arises from
the semi-geometric construction of Kreck and Stolz. However, El has the
same Bousfield class at 2 as KO, so is not in any sense v2-periodic at
2. I point out that I understood tensor product theorems a little
better in this paper than I did in the Spin and KO paper, but not so
well as I did in the vn-elements paper. That is, if you want to
understand even the argument in the spin and KO paper, you should
probably look at this paper and the vn elements paper too.