In Fate/stay night: Heaven's feel III, why does Kirei end the chant against Zouken, with the greek "Κύριε ελέησον" (kyrie eleison)?
It means "O Lord show mercy"
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It's because of Christian liturgy. The "Kyrie eleison" is the name of a prayer, and one of the most ancient of gregorian chants.
It has its origins in Eastern Christian doctrine, it derives from ἐλέησόν με κύριε (eleison me kyrie), which was the Greek translation of a Biblical phrase often found in the Psalms: חָנֵּנִי יְהוָה, "have mercy on me, Lord". It's used as part of the litany, which is prayer that consists of petition to God or to a Saint to intercede, as the priest asks the petition, the chorus would answer "Kyrie eleison and "Christe eleison" in alternation.
So it seems fitting that for Fate worlds, where Christian doctrine is also a form of Magecraft, this chant is used as an incantation part of exorcism rituals, as it's asking for God to lend his power.