Although it is permissible to cook on Yom Tov, this heter is limited to cooking for other Jews. Because of this prohibition, Chazal were concerned that if one had non Jews as guests, he would cook extra for them. They therefore disallowed inviting non jews on Yom Tov, SA, OC 512:1.(However, they allowed them on Shabbos, see Tur OC: 325). The law is that a Jew who openly violates the Sabbath would also be prohibited to cook for, so he would also be included in the prohibition against inviting gentiles. What is the rationale for the common practice of inviting irreligious jews for the Seder and other Yom Tov meals. Is it permissible for Kiruv purposes? Is it always permissible? Is there any heter to actually cook food for him? Is this a rabbinic or biblical prohibition? Can one at least do chazarah for him?