  We study the ranges of the maps of convolution $u\otimes v\mapsto u\ast v$
and a `twisted' convolution $u\otimes v\mapsto u\ast \check{v}$
($\check{u}(s)=u(s^{-1})$) and on the Haagerup tensor product of a Fourier
algebra of a compact group $A(G)$ with itself. We compare the results to result
of factoring these maps through projective and operator projective tensor
products. We notice that $(A(G),\ast)$ is an operator algebra and observe an
unexpected set of spectral synthesis.
