For some reason I have created my Stack Overflow account linked from my Google account. Can I create a Stack Exchange account and connect my existing Stack Overflow account to the new one and unlink it from Google?
Click "my logins" and then "add more logins" from your profile while signed in. You can register for a Stack Exchange OpenID there and it will be added to your account. You can then remove the Google credentials.
If the association doesn't quite work, give us a shout via https://stackoverflow.com/contact and we can merge the profiles for you.