I found the stack alert extension on the chrome web store, but I have trouble setting it up.
I always get the following message when I click on its button:
So it seems to me that the cookie isn't shared.
What should I try now?
Click on the Extension icon. A popup will come which will allow the extension to fetch the oAUth key and Authenticate.
Once you click on Authorize, it should ask your to Approve the authorization. If this button isn't shown first try logging into Stack Exchange openID endpoint, if you're using that.
If you don't see the Extension Icon, head over to