The logs for Google Drive shows that activity responsible for “telling” the Google Play Store to install apps is
com.google.android.apps.docs/com.google.android.apps.docs.app.PhoneskyApplicationInstallerActivity
which, apparently, “tells”
com.android.vending/com.google.android.finsky.billing.lightpurchase.LightPurchaseFlowActivity
to install required packages.
So, theoretically, one could create an intent
Intent intent = new Intent("com.android.vending.billing.PURCHASE");
intent.setClassName("com.android.vending",
"com.google.android.finsky.billing.lightpurchase.LightPurchaseFlowActivity");
intent.putExtra(EXTRA_NAME, EXTRA_VALUE);
startActivityForResult(intent, 0);
with correct extra values and voilĂ !
However, calling LightPurchaseFlowActivity from non-Google signed app is failing, because they are, again apparently (according to the logs), checking the calling package’s signature:
W/Finsky(13209): [1] LightPurchaseFlowActivity.setupFromExternalPurchaseIntent: Called from untrusted package.
So, there, this can not be achieved at this moment.