This is a way of [programatically installing APKs][1]

the code snippet you're looking for is:

    Intent intent = new Intent(Intent.ACTION_VIEW);
    intent.setDataAndType(Uri.fromFile(new File(Environment.getExternalStorageDirectory() + "/download/" + "app.apk")),"application/vnd.android.package-archive");
    startActivity(intent);


  [1]: https://stackoverflow.com/questions/4967669/android-install-apk-programmatically/4969421#4969421