There are some incoherences when the use of a the group managers in the front-office.

Firstly, should there not be site-aware group managers as there are site-aware user managers?

Secondly, if I use a ModifiableJdbcGroupsManager with a site-aware user manager, the GroupsManager stores the login without @site suffix (logical, because it uses the UsersManager API).
This means a user cannot belong to a group in a specific site: if I have two accounts in two sites "user@site1" and "user@site2", after adding "user" in the Groups_Users table, the user can access the pages with limited access to the group both in site1 and site2.