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Wireless powered mobile edge computing (WP-MEC) has been recognized as a promising technique to provide both enhanced computational capability and sustainable energy supply to massive low-power wireless devices. However, its energy consumption becomes substantial, when the transmission link used for wireless energy transfer (WET) and for computation offloading is hostile. To mitigate this hindrance, we propose to employ the emerging technique of intelligent reflecting surface (IRS) in WP-MEC systems, which is capable of providing an additional link both for WET and for computation offloading. Specifically, we consider a multi-user scenario where both the WET and the computation offloading are based on orthogonal frequency-division multiplexing (OFDM) systems. Built on this model, an innovative framework is developed to minimize the energy consumption of the IRS-aided WP-MEC network, by optimizing the power allocation of the WET signals, the local computing frequencies of wireless devices, both the sub-band-device association and the power allocation used for computation offloading, as well as the IRS reflection coefficients. The major challenges of this optimization lie in the strong coupling between the settings of WET and of computing as well as the unit-modules constraint on IRS reflection coefficients. To tackle these issues, the technique of alternative optimization is invoked for decoupling the WET and computing designs, while two sets of locally optimal IRS reflection coefficients are provided for WET and for computation offloading separately relying on the successive convex approximation method. The numerical results demonstrate that our proposed scheme is capable of monumentally outperforming the conventional WP-MEC network without IRSs.