Q. See question 2895 above regarding building a columbarium. If the building owner can get a permit for installing a crematorium in that building, would that be also permitted in need?
A. Some Poskim maintain that even for the Jewish dead, the mitzva of burial is only Rabbinical. (Rambam - H. Avel 14, Chavas Yoir - Y.D. 31, see Yabia Omer Y.D. 3: 23.
Other Poskim maintain that there is a mitzva for Gentiles to bury their own dead. K'lei Chemda (Chayei Sarah) quoting Avnei Nezer mentions that Gentiles have an obligation to bury their dead, since they are also obliged to return something taken from others (hashovas hagezeilah), and the mitzva of burial is based on the returning to the planet earth of what was taken from it.
Nevertheless, in principle there may not be a mitzva for Jews of burial on a Gentile's body (Meiri Shabbos 94a quoting Yerushalmi, Beis Yitzchok (24: 4) Mishne Halochos (7: 63). Unless it involves 'darkei shalom' or maintaining equality, egalitarian rights and peace for all (Gittin 61a). That may not be the case when a Gentile actually demands cremation.
However, Horav Shlomo Miller Shlit'a pointed out to that Tzitz Eliezer (10: 25: 9) quoting Ramban, Chavas Yoir and Chassam Sofer, is stringent and maintains that not only in Eretz Yisroel, but also in Chutz L'aretz there is an obligation, besides 'darkei shalom' to bury all dead. Besides there is the additional consideration that the dead one may have been actually Jewish.
The Rov therefore, maintains that one should abstain from engaging in the cremation of any corpses.
Rabbi A. Bartfeld as advised By Horav Shlomo Miller and Horav Aharon Miller Shlit'a