I have preference screen extended PreferenceActivity. For targeting OS 4.0.3, I wanted to add < icon on action bar so I did this in onCreate().
ActionBar actionBar = getActionBar();
actionBar.setHomeButtonEnabled(true);
actionBar.setDisplayHomeAsUpEnabled(true);
It worked. < was added to left of app icon. But when I tap the item which goes into the next level (more detail screen), the < won't be displayed. Returning to the top level, the < appears again.
I have never thought about a mechanism of nested preference since smart the PreferenceActivity hides it. Now my question is, why  won't PreferenceActivity display the < on nested preference?
I don't want to argue that I don't need to add < to the preference screen. (Even some of Google's app add, some don't, so I think there is no solid rule for this.)
If there is a simple solution for this, I want to solve this issue.
Instead of dynamically adding this, you should add the arrow by writing a custom ActionBar style to be used with your application theme. (Basically, see https://stackoverflow.com/a/16247111/582004)
This is my working code for Home button on Settings activity
    @Override   
    public void onCreate(Bundle savedInstanceState) {
    super.onCreate(savedInstanceState);
    LinearLayout root = (LinearLayout)findViewById(android.R.id.list).getParent().getParent().getParent();
    Toolbar bar = (Toolbar) LayoutInflater.from(this).inflate(R.layout.settings_toolbar, root, false);
    root.addView(bar, 0); // insert at top
    bar.setTitle("Settings");
    bar.setTitleTextColor(Color.WHITE);
    bar.setNavigationOnClickListener(new View.OnClickListener() {
        @Override
        public void onClick(View v) {
            finish();
        }
    });
    addPreferencesFromResource(R.layout.settings);
}
This is the settings_toolbar.xml
    <android.support.v7.widget.Toolbar xmlns:android="http://schemas.android.com/apk/res/android"
xmlns:app="http://schemas.android.com/apk/res-auto"
android:id="@+id/toolbar"
android:layout_width="match_parent"
android:layout_height="?attr/actionBarSize"
android:background="@color/colorPrimary"
android:elevation="2dp"
android:fitsSystemWindows="true"
android:minHeight="?attr/actionBarSize"
app:navigationIcon="@drawable/gobackleftarrow"
app:theme="@style/ThemeOverlay.AppCompat.Dark.ActionBar">
</android.support.v7.widget.Toolbar>
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