High peak-to-average power ratio (PAPR) has been major drawback of orthogonal frequency-division multiplexing (OFDM). To reduce the PAPR in the polar-coded OFDM systems, we propose a polar coding-based selective mapping (SLM) which does not transmit redundant information. Based on a set of independent frozen data blocks, we construct coset codes of a linear polar code to efficiently generate multiple OFDM signals, and selectively transmit the one with the lowest PAPR. Since the proposed SLM does not transmit either the side information or PAPR control labels, we can avoid the data rate loss. We also present an adaptive trial-based blind receiver to perform not only decoding of the unfrozen data block but also detection of the selected signal (or frozen data block). Simulation results show that the PAPR performance of the proposed SLM can approach to the optimal, and the blind receiver can support the proposed SLM with high accuracy.