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In this paper, we investigate a relay-assisted resource sharing scenario, namely, multi-operator two-way relaying with a MIMO amplify-and-forward (AF) relay. Here, the spectrum and the relay (infrastructure) are shared among multiple operators. We develop the projection based separation of multiple operators (ProBaSeMo) relay transmit strategy, which is inspired by the block diagonalization (BD) and regularized block diagonalization (RBD) schemes that are space-division multiple access (SDMA) approaches for multi-user MIMO systems. If the user terminals are equipped with multiple antennas, appropriate precoding and decoding matrix designs are also proposed. Compared to the time-shared approach where the relay is used by different operators in a time division multiple access (TDMA) manner, we demonstrate that the ProBaSeMO algorithms can provide a significant sharing gain in terms of the sum rate with many antennas at the relay or in the high SNR regime in a two-operator case. For a fixed number of antennas at the relay, an even higher sharing gain can be obtained if the number of operators increases.