Can we build some sort of ventilation system in our rental apartment?

Question

There isn't an exhaust fan in our kitchen. Everytime we fry or bake something we set off the smoke detector. There's a window pretty close to our kitchen. Is there a way to rig up some sort of flexible exhaust tubing and a fan so that we can draw the smoke out our window?

Answer 1

Is it sufficient to put a window fan in the window when cooking?

If not, there are ductless range hoods, also known as recirculating range hoods. These filter the air and lets it back out in the room.