On Künneth suspensions

In (2) we defined the Künneth suspension of a cohomology operation —the Künneth suspension involves an arbitrary css-complex Y rather than the 1-sphere S 1 , as with the usual suspension of a cohomology operation. Now the suspension homomorphism is well known to be related to the operation of forming loop spaces (cf. (4)). The main object of this paper is to prove a similar result for the Künneth suspension.