Stable cohomology is a Z-graded multiplicative cohomology theory generalizing Tate cohomology and first defined by Pierre Vogel. It is connected through a short exact sequence to absolute cohomology and bounded cohomology. In this talk we investigate the structure of the bounded cohomology as a graded bimodule using the Hopf algebra structure of the Ext algebra. We use the information on the bimodule structure of bounded cohomology to study the stable cohomology algebra as a trivial extension algebra.