Where does “жилетка” come from?

жилетка (Russian) comes from Russian жиле́т, from French gilet, from Italian giulecco, from Turkish yelek, from Ottoman Turkish یلك, from Old Anatolian Turkish يَلَك, from Old Anatolian Turkish يَل, from Old Turkic 𐰘𐰠 — wind.

жилетка (Russian): vest