For locally compact groups
G and
H let
A(G) denote the Fourier algebra of
G and
B(H) the Fourier–Stieltjes algebra of
H. Any continuous piecewise affine map
α:Y
H→G (where
Y is an element of the open coset ring) induces a completely bounded homomorphism
Φα:A(G)→B(H) by setting
Φαu