  Given a family of monodromy matrices {T_u; u=0,1,...,K-1} corresponding to
integrable anisotropic vertex models of A_{(n_u)-1}-type, we build up a related
mixed vertex model by means of glueing the lattices on which they are defined,
in such a way that integrability property is preserved. Algebraically, the
glueing process is implemented through one dimensional representations of
rectangular matrix algebras A(R_p,R_q), namely, the `glueing matrices' zeta_u.
Here R_n indicates the Yang-Baxter operator associated to the standard Hopf
algebra deformation of the simple Lie algebra A_{n-1}. We show there exists a
pseudovacuum subspace with respect to which algebraic Bethe ansatz can be
applied. For each pseudovacuum vector we have a set of nested Bethe ansatz
equations identical to the ones corresponding to an A_{m-1} quasi-periodic
model, with m equal to the minimal range of involved glueing matrices.
