Notification/push when geofencing in background

I'm developing an application where I use a geofencing module (https://github.com/aaronksaunders/ci.geofencing) that triggers an event when a user has entered a specific area. This monitoring works in both active and background mode.

So far so good.

The part I'm not sure about is how to send an alert to the user when the app is not actively used.

Example: the user activates the geofence based reminder, backgrounds the app, and enters the reminder area some hours later -- and should at that point receive a push-like alert with a predefined message.

Code:

ci_geofencing.startGeoFencing(regions, function(event) {
 
    if(event.type === 'entered_region') {
        //user entered the region.
        //If the app is backgrounded, I'd like to send some sort of push-like message to the user.
    };
 
});

Does anyone know if what I'm looking for is possible?

Any help is very much appreciated.

Application Type: Mobile SDK: 3.2.1 Platform: iOS 6