  The path space of an inhomogeneous vertex model constructed from the vector
representation of $U_q\bigl(gl(2|2)\bigr)$ and its dual is studied for various
choices of composite vertices and assignments of $gl(2|2)$-weights. At $q=0$,
the corner transfer matrix Hamiltonian acts trigonally on the space of
half-infinite configurations subject to a particular boundary condition. A
weight-preserving one-to-one correspondence between the half-infinite
configurations and the weight states of a level-one module of
$U_q\bigl(\hat{sl}(2|2)\bigr)/{\cal H}$ with grade $-n$ is found for $n\geq-3$
if the grade $-n$ is identified with the diagonal element of the CTM
Hamiltonian. In each case, the module can be decomposed into two irreducible
level-one modules, one of them including infinitely many weight states at fixed
grade. Based on a mapping of the path space onto pairs of border stripes, the
character of the reducible module is decomposed in terms of skew Schur
functions. Relying on an explicit verification for simple border stripes, a
correspondence between the paths and level-zero modules of
$U_q\bigl(\hat{sl}(2|2)\bigr)$ constructed from an infinite-dimensional
$U_q\bigl(gl(2|2)\bigr)$-module is conjectured.
