Where does “желетке” come from?

желетке (Kazakh) comes from Russian жилетка, 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 — wind.

желетке (Kazakh): vest, waistcoat