This plugin integrates google into elgg 1.8.

Allow user to login using google account.

You can shorten urls using users google account.

If you are using event calendar plugin then you can use this plugin to add the event to users

google calendar as well.

If you are using tasks plugin then you can use this plugin to add the even to users

tasks as well.

Please note this is an api plugin which means I provide with functions.To implement all the features you need to add code to your plugins.