  Thin superconducting YBa$_{2}$Cu$_{3}$O$_{7-\delta}$ films are patterned with
a vortex-pin lattice consisting of columnar defect regions (CDs) with 180 nm
diameter and 300 nm spacing. They are fabricated by irradiation with 75 keV
He$^+$ ions through a stencil mask. Peaks of the critical current reveal the
commensurate trapping of vortices in domains near the edges of the sample. Upon
ramping an external magnetic field, the positions of the critical current peaks
are shifted from their equilibrium values to lower magnetic fields in virgin
and to higher fields in field-saturated down-sweep curves, respectively. Based
on previous theoretical predictions, this irreversibility is interpreted as a
nonuniform, terrace-like critical state, in which individual domains are
occupied by a constant number of vortices per pinning site. The
magnetoresistance, probed at low current densities, is hysteretic and angle
dependent and exhibits minima that correspond to the peaks of the critical
current. The minima's positions scale with the component of the magnetic field
parallel to the axes of the CDs, as long as the tilted vortices can be
accommodated within the CDs. This behavior, different from unirradiated films,
confirms that the CDs dominate the pinning.
