Igniting an Oven from Afar

Greetings, regarding the issue of non-Jewish cooking, the author of the Shulchan Aruch and the Remo disagreed on whether a Jew's ignition of the fire upon which the food is cooked renders the food Jewish (and thus permitted; cooked food prepared solely by a non-Jew is forbidden). In the commentary of the Vilna Gaon, it is implied that in an oven, just lighting it is enough because “his power is like his body” (that is, a direct result of his action is considered an action of his body), and “his fire is considered his arrow” (that is, a fire ignited by a person is considered his own direct action). Hence, today there are places where only the kashruth supervisor can ignite the fire from afar [from his home] via the internet and so on. Is this effective for making this food permitted?

Dear …!
Indeed, remote ignition is as effective as ignition by hand.

See the book 'Mishmeres HaBayis' (by Rabbi Moshe Karp, pg. 31)