Operator biflatness of the Fourier algebra and approximate indicators for subgroups

We investigate if, for a locally compact group G, the Fourier algebra A(G) is biflat in the sense of quantized Banach homology. A central rôle in our investigation is played by the notion of an approximate indicator of a closed subgroup of G: The Fourier algebra is operator biflat whenever the diagonal in G×G has an approximate indicator. Although we have been unable to settle the question of whether A(G) is always operator biflat, we show that, for G=SL(3,C), the diagonal in G×G fails to have an approximate indicator.