The Auger Radio Detector (RD) will increase the sky coverage and overall aperture for mass-sensitive measurements of ultra-high-energy cosmic rays with the Pierre Auger Observatory. The installation of over 1600 dual-polarized short aperiodic loaded loop antennas (SALLAs) on an area of about 3000$\,$km$^2$ will enable the detection of highly inclined air showers via the emitted electromagnetic radiation in coincidence with the Auger water-Cherenkov detector array (SD). The combination of complementary information from both detectors yields a strong sensitivity to the mass composition of cosmic rays.

We will present the expected performance of the RD to detect and reconstruct inclined air showers. This study features comprehensive sets of Monte-Carlo generated air showers, utilizes a complete description of the instrumental response of the radio antennas, and in-situ recorded background. The estimation of an energy- and direction-dependent aperture yields an expectation of about 3900 events with energies above $10^{19}\,$eV being detected during 10 years of operation. From a full event reconstruction, we quantify the achievable energy resolution to be better than 10% at and beyond $10^{19}\,$eV. With this at hand, the potential to measure the number of muons and discriminate between different cosmic-ray primaries in combination with the SD using inclined air showers is presented. The discrimination between proton- and iron-induced air showers yields a figure-of-merit of 1.6.