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Let BG be a classifying variety for an exceptional simple simply connectedalgebraic group G. We compute the degree 3 unramified Galois cohomology of BGwith values in Q/Z(2) over an arbitrary field F. Combined with a paper byMerkurjev, this completes the computation of these cohomology groups for Gsemisimple simply connected over all fields.  These computations provide another example of a simple simply connected groupG such that BG is not stably rational

Unramified cohomology of classifying varieties for exceptional simply connected groups