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Using density-functional theory in the restricted-orientation approximation, we analyze the liquid-crystal patterns and phase behavior of a fluid of hard rectangular particles confined in a two-dimensional square nanocavity of side length H composed of hard inner walls. Patterning in the cavity is governed by surface-induced order as well as capillary and frustration effects and depends on the relative values of the particle aspect ratio kappa = L/sigma, with L the length and sigma the width of the rectangles (L >= sigma), and cavity size H. Ordering may be very different from bulk (H -> infinity) behavior when H is a few times the particle length L (nanocavity). Bulk and confinement properties are obtained for the cases kappa = 1, 3, and 6. In bulk the isotropic phase is always stable at low packing fractions eta = L sigma rho(0) (with rho(0) the average density) and nematic, smectic, columnar, and crystal phases can be stabilized at higher eta depending on kappa: For increasing eta the sequence of isotropic to columnar is obtained for kappa = 1 and 3, whereas for kappa = 6 we obtain isotropic to nematic to smectic (the crystal being unstable in all three cases for the density range explored). In the confined fluid surface-induced frustration leads to fourfold symmetry breaking in all phases (which become twofold symmetric). Since no director distortion can arise in our model by construction, frustration in the director orientation is relaxed by the creation of domain walls (where the director changes by 90 degrees); this configuration is necessary to stabilize periodic phases. For kappa = 1 the crystal becomes stable with commensurate transitions taking place as H is varied. These transitions involve structures with different number of peaks in the local density. In the case kappa = 3 the commensurate transitions involve columnar phases with different number of columns. In the case kappa = 6 the high-density region of ...