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Cherednik attached to an affine Hecke algebra module a compatible system ofdifference equations, called quantum affine Knizhnik-Zamolodchikov (KZ)equations. In case of a principal series module we construct a basis of powerseries solutions of the quantum affine KZ equations. Relating the bases fordifferent asymptotic sectors gives rise to a Weyl group cocycle, which wecompute explicitly in terms of theta functions. For the spin representation ofthe affine Hecke algebra of type C the quantum affine KZ equations become theboundary qKZ equations associated to the Heisenberg spin-1/2 XXZ chain. We showthat in this special case the results lead to an explicit 4-parameter family ofelliptic solutions of the dynamical reflection equation associated to Baxter's8-vertex face dynamical R-matrix. We use these solutions to define an explicit9-parameter elliptic family of boundary quantum Knizhnik-Zamolodchikov-Bernard(KZB) equations.

Connection problems for quantum affine KZ equations and integrable lattice models