Let BG be a classifying variety for an exceptional simple simply connected algebraic group G. We compute the degree 3 unramified Galois cohomology of BG with values in (Q/Z)'(2) over an arbitrary field F. Combined with a paper by Merkurjev (Ann. Sci. Ecole Norm. Sup., 4-e serie, 35 (2002), 445--476), this completes the computation of these cohomology groups for G semisimple simply connected over all fields.

These computations provide another example of a simple simply connected group G such that BG is not stably rational. this completes the computation of these cohomology groups for G semisimple simply connected over all fields.

Preprint version (15 August 03 / only small changes from the arXiv version and the published version)
(dvi) (ps) (pdf)