java.lang.NoClassDefFoundError at Runtime in Activity's inner class

问题

I have found a lot of similar questions, but no one helps me.

I have next problem. I have complete project for Android and I have to export it's functionality to .aar library. First of all I created new project and created new module where put my source project. At this step all things goes well and I get my mylib.aar file in /build/outputs/aar/ folder. Then I created new project to test my mylib.aar, so I created libs folder under my app folder in Android Studio, and in build.gradle file of my test project I added these lines:

repositories {
    flatDir {dirs 'libs'}
}

dependencies {
    compile(name: 'mylib', ext: 'aar')
}

In manifest file I added declaration of MainActivity from library:

<activity android:name="com.testlib.mylib.MainActivity"
            android:label="MainActivity"/>

Android Studio found this file well and I even can watch source code through built-in decompiler. But when I try to start this activity from another activity that isn't placed in my lib I get this error:

3838-3838/com.testapp.testsdkapp E/AndroidRuntime﹕ FATAL EXCEPTION: main
    Process: com.testapp.testsdkapp, PID: 3838
    java.lang.NoClassDefFoundError: com.testlib.mylib.MainActivity$RegisterInBackgroundTask
            at com.testlib.mylib.MainActivity.registerInBackground(MainActivity.java:1551)
            at com.testlib.mylib.MainActivity.onCreate(MainActivity.java:269)
            at android.app.Activity.performCreate(Activity.java:5937)
            at android.app.Instrumentation.callActivityOnCreate(Instrumentation.java:1105)
            at android.app.ActivityThread.performLaunchActivity(ActivityThread.java:2251)
            at android.app.ActivityThread.handleLaunchActivity(ActivityThread.java:2360)
            at android.app.ActivityThread.access$800(ActivityThread.java:144)
            at android.app.ActivityThread$H.handleMessage(ActivityThread.java:1278)
            at android.os.Handler.dispatchMessage(Handler.java:102)
            at android.os.Looper.loop(Looper.java:135)
            at android.app.ActivityThread.main(ActivityThread.java:5221)
            at java.lang.reflect.Method.invoke(Native Method)
            at java.lang.reflect.Method.invoke(Method.java:372)
            at com.android.internal.os.ZygoteInit$MethodAndArgsCaller.run(ZygoteInit.java:899)
            at com.android.internal.os.ZygoteInit.main(ZygoteInit.java:694)

RegisterInBackgroundTask is inner public AsyncTask class declared in my MainActivity in the library. I tried to put mylib.aar in aar folder and declare in build.gradle in other way, but it didn't help me and I get similar error.

If this information is not enough, I'll add required parts of code etc. So please help me, if you know how to solve my problem! Thanks.