Claude Cibils Tensor product of Hopf bimodules over a group algebra . \`a para\^itre dans Proceedings American Math. Society. Pr\'epublication 320 de l'Institut Fourier (1995). Overview. The monoidal structure of Hopf bimodules over a group algebra can be completely described by means of the structure constants, depending on the conjugacy classes. These results provides an interesting analogy with the comparison between the Hochschild ring cohomology of the group algebra, and the usual ring cohomology of the group.