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Jan 11, 2010 at 16:42 comment added Qiaochu Yuan An important point to make here is that the tensor product structure on R(G) comes from the comultiplication on C[G], which means you then have to ask yourself: where did the multiplication go?
Jan 11, 2010 at 16:35 history edited Theo Johnson-Freyd CC BY-SA 2.5
corrected major errors
Jan 11, 2010 at 16:23 comment added Theo Johnson-Freyd oops! I wasn't thinking.
Jan 11, 2010 at 6:44 comment added Mariano Suárez-Álvarez The representation ring $R(G)$ from the question is not the group algebra, as far as I can see, and it is the latter which is a bialgebra.
Jan 10, 2010 at 20:54 comment added Kevin Buzzard Thanks Theo, that's a great comment. You've elucidated a point which I only had a much vaguer appreciation of when I wrote my answer.
Jan 10, 2010 at 20:03 history answered Theo Johnson-Freyd CC BY-SA 2.5