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Fast radio bursts (FRBs) are a new kind of extragalactic radio transients. Some of them show repeating behaviors. Recent observations indicate that a few repeating FRBs (e.g., FRB 121102) present time–frequency downward drifting patterns and nearly 100% linear polarization. Following the model of Dai et al. who proposed that repeating FRBs may originate from a slowly rotating, old-aged pulsar colliding with an asteroid belt around a stellar-mass object, we focus on the prediction of time–frequency drifting and polarization. In this scenario, the frequency drifting is mainly caused by the geometric structure of a pulsar magnetosphere, and the drifting rate–frequency index is found to be 25/17. On the other hand, by considering the typical differential mass distribution of incident asteroids, we find that an asteroid with mass m ≳ 1017 g colliding with the pulsar would contribute abundant gravitational energy, which powers an FRB. A broad frequency band of the FRBs would be expected, due to the mass difference of the incident asteroids. In addition, we simulate the linear polarization distribution for the repeating FRBs, and constrain the linear polarization with ≳30% for the FRBs with flux of an order of magnitude lower than the maximum flux. [ABSTRACT FROM AUTHOR]