The current Moodle calendar event web services return a list of events by site, course or use (and module).
The app should inform users via local notifications of this events, even when the app is in background.

There is a Cordova plugin for local notifications widely use that support ios, android and wp8:
https://github.com/katzer/cordova-plugin-local-notifications

Required changes in the app:

• Calendar events should be synchronized periodically in the background or when the app is open/reopened (if the device is old and does not support background processes)
• We must add support to groups in the calendar events. We need to retrieve all the course groups a user belongs to.
• New events should be added in the app as local notifications using the plugin.
• The user must enable/disable this feature for all the notifications or specific ones (disable all local notifications or specific ones)