The phrase "put the air" can be replaced with a number of synonyms depending on the context. For example, "inflate" is a common synonym that can be used when referring to inflating a tire or a balloon. "Fill" is another synonym that can be used when referring to filling a tire or a ball with air. "Pump up" is also a synonym that can be used when inflating a tire or a ball. "Charge" is often used when referring to charging an air compressor or a scuba tank. Finally, "aerate" can be used when referring to adding oxygen to a room or an outdoor space.