  The Fourier(-Stieltjes) algebras on locally compact groups are important
commutative Banach algebras in abstract harmonic analysis. In this paper we
introduce a generalization of the above two algebras via twisting with respect
to 2-cocycles on the group. We also define and investigate basic properties of
the associated multiplier spaces with respect to a pair of 2-cocycles. We
finally prove a twisted version of the result of Bo\.{z}ejko/Losert/Ruan
characterizing amenability of the underlying locally compact group through the
comparison of the twisted Fourier-Stieltjes space with the associated
multiplier spaces.
