  Usually quantum chains with quantum group symmetry are associated with
representations of quantized universal algebras $U_q(g) $ . Here we propose a
method for constructing quantum chains with $C_q(G)$ global symmetry , where
$C_q(G)$ is the algebra of functions on the quantum group. In particular we
will construct a quantum chain with $GL_q(2)$ symmetry which interpolates
between two classical Ising chains.It is shown that the Hamiltonian of this
chain satisfies in the generalised braid group algebra.
