  For a finitely aligned k-graph $\Lambda$ with X a set of vertices in
$\Lambda$ we define a universal C*-algebra called $C^*(\Lambda,X)$ generated by
partial isometries. We show that $C^*(\Lambda,X)$ is isomorphic to the corner
$P_XC^*(\Lambda)P_X$, where $P_X$ is the sum of vertex projections in X. We
then prove a version of the Gauge Invariant Uniqueness Theorem for
$C^*(\Lambda,X)$, and then use the theorem to prove various results involving
fullness, simplicity and Morita equivalence as well as new results involving
symbolic dynamics.
