You need to override the default behavior of android.R.id.home to onBackPressed.

class SettingsActivity : AppCompatActivity() {

    ...

    override fun onOptionsItemSelected(item: MenuItem): Boolean {
        return when (item.itemId) {
            android.R.id.home -> {
                onBackPressed()
                true
            }
            else -> super.onOptionsItemSelected(item)
        }
    }

    ...

Found a good complete example here https://github.com/googlearchive/android-preferences

I am trying to implement preferences using multiple screens. The action bar back button only returns to MainActivity even for sub preference screens. For example, I have a root preference screen and then a sub reference screen. The back button on the root preference screen goes back to the main activity as expected. But the back button on the sub reference screen also goes back to the main activity rather than the root preference screen. Below is a code dump because I’m not sure what I am doing wrong. Thanks.

Androidmanifest.xml

<?xml version="1.0" encoding="utf-8"?>
<manifest xmlns_android="http://schemas.android.com/apk/res/android"
    package="com.example.PreferencesTest">

    <application
        android_allowBackup="true"
        android_icon="@mipmap/ic_launcher"
        android_label="@string/app_name"
        android_roundIcon="@mipmap/ic_launcher_round"
        android_supportsRtl="true"
        android_theme="@style/AppTheme">
        <activity
            android_name=".SettingsActivity2"
            android_label="@string/title_activity_settings2"
            android_parentActivityName=".SettingsActivity">
            <meta-data
                android_name="android.support.PARENT_ACTIVITY"
                android_value=".SettingsActivity" />
        </activity>
        <activity
            android_name=".SettingsActivity"
            android_label="@string/title_activity_settings"
            android_parentActivityName=".MainActivity">
            <meta-data
                android_name="android.support.PARENT_ACTIVITY"
                android_value=".MainActivity" />
        </activity>
        <activity
            android_name=".MainActivity"
            android_theme="@style/AppTheme.Launcher">
            <intent-filter>
                <action android_name="android.intent.action.MAIN" />
                <category android_name="android.intent.category.LAUNCHER" />
            </intent-filter>
        </activity>
    </application>
</manifest>

MainActivity.kt

class MainActivity : AppCompatActivity()
{
    override fun onCreate(savedInstanceState: Bundle?)
    {
        setTheme(R.style.AppTheme)
        super.onCreate(savedInstanceState)
        setContentView(R.layout.activity_main)
    }

    //Inflates settings menu button
    override fun onCreateOptionsMenu(menu: Menu): Boolean
    {
        val inflater: MenuInflater = menuInflater
        inflater.inflate(R.menu.settings_menu, menu)
        return true
    }

    override fun onOptionsItemSelected(item: MenuItem): Boolean
    {
        return when(item.itemId)
        {
            R.id.action_settings ->
            {
                val intent = Intent(this, SettingsActivity::class.java)
                startActivity(intent)
                true
            }
            else -> super.onOptionsItemSelected(item)
        }
    }
}

SettingsActivity.kt

class SettingsActivity : AppCompatActivity()
{

    override fun onCreate(savedInstanceState: Bundle?)
    {
        super.onCreate(savedInstanceState)
        setContentView(R.layout.settings_activity)

        supportFragmentManager
            .beginTransaction()
            .replace(R.id.settings, SettingsFragment())
            .commit()

        supportActionBar?.setDisplayHomeAsUpEnabled(true)

    }

    class SettingsFragment : PreferenceFragmentCompat()
    {
        override fun onCreatePreferences(savedInstanceState: Bundle?, rootKey: String?)
        {
            setPreferencesFromResource(R.xml.root_preferences, rootKey)
        }
    }
}

SettingsActivity2.kt

class SettingsActivity2 : AppCompatActivity() {

    override fun onCreate(savedInstanceState: Bundle?) {
        super.onCreate(savedInstanceState)
        setContentView(R.layout.settings_activity)
        supportFragmentManager
            .beginTransaction()
            .replace(R.id.settings, SettingsFragment())
            .commit()
        supportActionBar?.setDisplayHomeAsUpEnabled(true)
    }

    class SettingsFragment : PreferenceFragmentCompat() {
        override fun onCreatePreferences(savedInstanceState: Bundle?, rootKey: String?) {
            setPreferencesFromResource(R.xml.preferences2, rootKey)
        }
    }
}

res > menu > settings_menu.xml

<?xml version="1.0" encoding="utf-8"?>
<menu xmlns_android="http://schemas.android.com/apk/res/android"
    xmlns_app="http://schemas.android.com/apk/res-auto">

    <item
        android_id="@+id/action_settings"
        android_orderInCategory="100"
        android_title="Settings"
        app_showAsAction="ifRoom" />

</menu>

res > xml > root_preferences.xml

<?xml version="1.0" encoding="utf-8"?>
<PreferenceScreen xmlns_android="http://schemas.android.com/apk/res/android"
    xmlns_app="http://schemas.android.com/apk/res-auto">
    <Preference
        android_fragment="com.example.PreferencesTest.SettingsActivity2$SettingsFragment"
        android_title="Title"
        android_summary="Summary">
        <extra
            android_name="name"
            android_value="preferences2" />
    </Preference>
</PreferenceScreen>

res > xml > preferences2.xml

<?xml version="1.0" encoding="utf-8"?>
<PreferenceScreen xmlns_android="http://schemas.android.com/apk/res/android"
    xmlns_app="http://schemas.android.com/apk/res-auto">
    <EditTextPreference
        app_key="callNumber"
        app_title="Call Number"
        android_inputType="phone"
        app_useSimpleSummaryProvider="true" />
</PreferenceScreen>