  Let $A(G)$ and $B(H)$ be the Fourier and Fourier-Stieltjes algebras of
locally compact groups $G$ and $H$, respectively. Ilie and Spronk have shown
that continuous piecewise affine maps $\alpha: Y \subseteq H\rightarrow G$
induce completely bounded homomorphisms $\Phi:A(G)\rightarrow B(H)$, and that
when $G$ is amenable, every completely bounded homomorphism arises in this way.
This generalised work of Cohen in the abelian setting. We believe that there is
a gap in a key lemma of the existing argument, which we do not see how to
repair. We present here a different strategy to show the result, which instead
of using topological arguments, is more combinatorial and makes use of measure
theoretic ideas, following more closely the original ideas of Cohen.
