BuddyPress Ajax registration modal provides various url tags that you can use in the redirect box. A tag is a text token demarcated by the []. A few tags may not be available in some contexts.

Available Tags:-

• [site.url] – Current blog’s home url, e.g http://example.com. Applicable context:- Login, Registration, Forget Password.
• [network.url]- If on multisite, it resolves to network’s home url. Applicable context:- Login, Registration, Forget Password.
• [user.url] :- The user’s profile url in the applicable context. Eg. http://example.com/members/sbrajesh/. Applicable context:- Login, Registration.
• [user.login]:- The user’s login username( e.g sbrajesh). Applicable context:- Login, Registration.
• [user.nicename]:- The user’s nicename(what you see in the url).
• [user.id]:- Numeric user id.

The user specific tags are only available in the login, registration context and not in the forget password context.