Final answer:
The protein responsible for the exchange of bicarbonate ions and chloride ions across the red blood cell membrane is band 3.
Step-by-step explanation:
The protein responsible for the exchange of bicarbonate ions and chloride ions across the red blood cell membrane is band 3. Bicarbonate leaves the red blood cells and enters the blood plasma, while chloride is transported back into the red blood cells. This exchange is known as the chloride shift and is important for the transport of carbon dioxide in the blood.