  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, 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.
