I recently saved a pigeon roadside. What can I do to take care of it and find it’s owner?

It is banded and VERY tame. It suffered trauma (I assume it was hit by a car). It will not use it’s left foot nor will it fly. Is there a way to locate the owner? Is it ok to keep it outside? Right now I have it in a hutch outside with some meadow grass(for bedding), the towel that I picked it up with, seed and bottled water in a dish. I do have some bird background but have never rescued a pigeon before. I have rescued/released 11 baby robins, 2 sparrows, etc., nothing older nor of this breed. PLEASE HELP! Thanks in advance!
By the way I live in Northern Ohio. Is climate an issue with them as we approach cooler months?

websites below will help in finding the pigeon’s owner.

Naaka-hay Rescue