You have to move the portion of the background task that updates the UI onto the main thread. There is a simple piece of code for this:

runOnUiThread(new Runnable() {

    @Override
    public void run() {

        // Stuff that updates the UI

    }
});

Documentation for Activity.runOnUiThread.

Just nest this inside the method that is running in the background, and then copy paste the code that implements any updates in the middle of the block. Include only the smallest amount of code possible, otherwise you start to defeat the purpose of the background thread.