  We propose a generalisation of Exel's crossed product by a single
endomorphism and a transfer operator to the case of actions of abelian
semigroups of endomorphisms and associated transfer operators. The motivating
example for our definition yields new crossed products, not obviously covered
by familiar theory. Our technical machinery builds on Fowler's theory of
Toeplitz and Cuntz-Pimsner algebras of discrete product systems of Hilbert
bimodules, which we need to expand to cover a natural notion of relative
Cuntz-Pimsner algebras of product systems.
