Asalamu Alaykum. Is it permissible for a Muslim to ask a non-Muslim to forgive you for wronging the non-Muslim?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.

It is impermissible for a Muslim to wrong any person, be it a Muslim or a non-Muslim. The Prophet, sallallaahu ‘alayhi wa sallam, said: "Indeed, whoever wrongs someone under treaty or degrades him or charges him above his capacity or takes something from him without consent, I am the one who will contend with him in a plea on the Day of Judgment." [Abu Daawood - Al-Albaani graded it Saheeh (sound)]

It is incumbent on the Muslim to seek forgiveness from the non-Muslim. If the Muslim dies before being forgiven by the non-Muslim whom he had wronged, the wronged non-Muslim will be avenged against the Muslim on the Day of Judgment given the general indication of the Hadeeth reported on the authority of Abu Hurayrah that the Prophet, sallallaahu ‘alayhi wa sallam, said: "Do you know who the bankrupt one is?" People said: "The bankrupt one among us is the one who has neither money nor property." He, sallallaahu ‘alayhi wa sallam, said: "The real bankrupt of my nation is the one who comes on the Day of Resurrection with prayer, fasting, and charity, having insulted such a one, slandered such a one, unlawfully devoured the wealth of such a one, shed the blood of such a one, and struck such a one; such a one will be given some of his good deeds, and such a one some of his good deeds. If his good deeds are exhausted before judgment is settled, he will receive their sins and they will be cast upon him, and then he will be cast into the Fire."

Moreover, Anas narrated that the Prophet, sallallaahu ‘alayhi wa sallam, said: "Beware of the supplication of the wronged person even if he is a disbeliever, for, indeed, there is no barrier between it and Allaah." [Ahmad; its Isnaad (chain of narrators) is Hasan (good)]

This Hadeeth affirms that the wronged non-Muslim has rights pertaining to the Muslim who wrongs him.