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It is proved that:  (1) The Fourier algebra A(G) of a simple Lie group G of real rank at least 2with finite center does not have a multiplier bounded approximate unit.  (2) The reduced C*-algebra of any lattice in a non-compact simple Lie groupof real rank at least 2 with finite center does not have the completely boundedapproximation property.  Hence, the results obtained by J. de Canniere and the author for SO(n,1), nat least 2, and by M. Cowling for SU(n,1) do not generalize to simple Liegroups of real rank at least 2.

Group C*-algebras without the completely bounded approximation property