Return to Revisions

There isn't one. The scaling operation that you describe (which would have to be an odd scale factor, by the way) doesn't commute with suspension. Cohomology is a "suspension-preserving" functor (there's probably some fancy way of saying this using triangulated categories) so when you consider a cohomology theory you should really think of the target as "graded algebras over the coefficient ring with a suspension operation" only that's not quite as snappy as "graded rings" so we tend to be a bit sloppy about saying it.