  An S-matrix satisying the Yang-Baxter equation with symmetries relevant to
the AdS_5xS^5 superstring has recently been determined up to an unknown scalar
factor. Such scalar factors are typically fixed using crossing relations,
however due to the lack of conventional relativistic invariance, in this case
its determination remained an open problem.
  In this paper we propose an algebraic way to implement crossing relations for
the AdS_5xS^5 superstring worldsheet S-matrix. We base our construction on a
Hopf-algebraic formulation of crossing in terms of the antipode and introduce
generalized rapidities living on the universal cover of the parameter space
which is constructed through an auxillary, coupling constant dependent,
elliptic curve. We determine the crossing transformation and write functional
equations for the scalar factor of the S-matrix in the generalized rapidity
plane.
