Groups will have the role to bring more stability to the currency.
Some ways groups could work:
A group of a small city: a number of business owners could come together to start such a group. They could have a centralized process where you would register by appearing physically in one of the businesses.
Centralized groups with a n out of m voters rule.
Decentralized groups where the majority/x% + quorum can add new member.
Web of trust rules.