Suppose that F/Q is a number field.

Using automorphic forms, Borel computed the (R-) stable cohomology of SL`_`n(O`_`F), and as a result, computed K`_`i(O`_`F) tensor Q. Nowadays, using work of Suslin, Voevodksy, Rost, etc, one has an almost "complete" understanding of the actual integral groups K`_`i(Z), say, modulo Vandiver's conjecture. This does not _directly_ give the stable cohomology of SL`_`n, because one set of groups is computing homotopy and the other is computing cohomology, but let us not worry about that distinction for the moment.

Borel also computed the (R-) stable cohomology of Sp`_`2n(O`_`F).
My question, loosely speaking, is whether one can describe the stable integral cohomology of Sp`_`2n(Z) in as detailed away as the algebraic K-groups of Z "describe" the integral cohomology of SL`_`n(Z).