Android : how to execute AsyncTask?

You need to create an instance of your DonwloadXML file and call execute() on that method:

DownloadXML task=new DownloadXML();
task.execute();

EDIT: you should probably also return the listOffers from your doInBackground() and process the array in the onPostExecute() method of your AsynTask. You can have a look at this simple AsyncTask tutorial.

you should call it like:

new DownloadXML().execute();