M, '- M°'-t Al", M; 1-* ... is exact. As an interesting byproduct of our work on united K-theory, we obtain a Kunneth theorem. 12 Theorem. For spectra X and Y, there is a natural short exact sequence K*RTX ®CiZT K* RTl' >- K* RT(X A Y) -* TorCRT(K* RTX, K* RTE') This Kunneth exact sequence need not be splittable, since it expresses KOl(MZ/2 A MZ/2) as a nontrivial extension of Z/2 by Z/2.
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