For years I have used OpenID delegation to log in to Stack Overflow (among other sites) using my own URI as OpenID but having Google handle the authentication. I use the te
Assuming that you want to use your own domain as the user supplied login identifier --
In addition, if StackOverflow supports OpenID Connect Migration 1.0, and assuming that Google returns your custom domain claimed_id in the Migration response, then:
would smooth your way.