This thread gives more info on what you can do if you find a 'lost' pigeon.
https://www.backyardchickens.com/threads/found-a-lost-pigeon-heres-what-to-do.1387573/
You are doing the right thing by providing food and water. Because of the bands I believe this is a racing homer who has stopped for rest and refreshments on its way home. Hard to know why. :confused: Most likely it will be on its way after a few days. If you catch/trap it you can read the...