Broken redirect with CB Connect 4.0.0 on mobile device

I use the new CB Connect, the great all in one Social connecter. All configuration-settings are sucessfully completed.
All Logins (FB, Twitter, G+) on Desktop-Devices works fine. No problems detected.

But same configuration on same site but with mobile device the login gets a blank page....
the current url is: www.mysite.ch/index.php?option=com_comprofiler&task=pluginclass&plugin=cbconnect&action=google&func=accesstoken&format=raw&code=and here my token....
after redirect from 3pd Site back to own site, the "success message" wont show. I see only a blank page and the current user is not logged in....

Tested Mobile Devices are: iPad 3rd Generation, Samsung Galaxy Note, iPhone 5 and Samsung Galaxy SIII

It's not designed for or tested on mobile devices. No where do we advertise it's for mobile and if we've mislead you please point us to where we have so we may correct the mistake.

ok, thank you for the answer....

To explain further the reason it's not going any further is it uses jQuery to display a popup window that handles the authentication. The blank page you're seeing is the final step of this authentication and jQuery is used to close this window. When the window closes a Callback is fired in jQuery that sends the user through the CB Connect registration functions. If this window isn't closed that never happens. I've no idea how mobile devices handle this type of behavior, but I assume if it's a full web browser like Chrome Mobile it might work ok.