Looks like you want to set the ActionBar's home button as your delete button. I would suggest not to do it as that is a bad design decision in my opinion. And moreover you also want to show the button on the right hand side which can be done in a much intuitive manner by using a menu.
Please have a look at the official documentaion for adding ActionBar actions here
Basically you need to add an XML menu resource and declare your actions like this:
<menu xmlns:android="http://schemas.android.com/apk/res/android" >
<item
android:id="@+id/action_delete"
android:icon="@drawable/ic_delete"
android:title="@string/action_delete"
app:showAsAction="always"/>
</menu>
Then in your Activity override the OnOptionsItemSelected method:
@Override
public boolean onOptionsItemSelected(MenuItem item) {
switch (item.getItemId()) {
case R.id.action_delete:
// Do your stuff here
return true;
default:
return super.onOptionsItemSelected(item);
}
}