The information in this questionChoose which Google Account when accessing Google Groups?is no longer currentI am signed into Google and in Gmail click a link to an invitation made to another of my email addresses. I tried adding that email to the Gmail account as an alias, but the Google group in question did not let me in.Must I ask the owner to resend to the Gmail account or can I sync/alias the other address to my Google account? I prefer to not use my main Gmail account for the list in question.
How do I accept an invitation to Google Groups sent to my other email address?
google groups
If you didn't yet added your desired email address as an alternate email address to your Google Account, do that first. See Sign in to your Google Account with another email address for details.Then, go to the group membership settings, and change the email address to be used for that group.From My membership settings - Google Groups HelpMy membership settingsYou can use your group membership settings to customize your name and  email address in a group, whether or not you show your photo and a  link to your Google profile, and how often you get email from the  group.Choose your group membership settings.Go to Google Groups.  Near the top left corner, click My Groups.  Find the name of the group > next to your name, click Edit.  Pick your settings using the Setting options and how to choose them section of this article.  In the lower left corner, click Save.