We have studied experimentally the influence of a parallel magnetic field ($B_{//}$) on microwave-induced resistance oscillations (MIRO) and zero-resistance states (ZRS) previously discovered in a high-mobility 2D electron system. We have observed a strong suppression of MIRO/ZRS by a modest $B_{//}sim 0.5$ T. In Hall bar samples, magnetoplasmon resonance (MPR) has also been observed concurrently with the MIRO/ZRS. In contrast to the suppression of MIRO/ZRS, the MPR peak is found to be enhanced by $B_{//}$. These findings have not been addressed by current models proposed to explain the microwave-induced effects.
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