On Android devices, all programs are installed thru some APK archives. Under Gnome Nautilus, these APK archives are recognised as a specific mime types and are displayed with some generic text file icon.
As most of the time the name of these APK archives is not very friendly, it is difficult to associate an APK file with the Android application it contains. To help you with this association, it could be very helpful to display the application icon as it is done under Android instead of the generic icon.
Thanksfully, under Gnome Shell, Nautilus allows to generate a specific thumbnail according to the APK mime type application/vnd.android.package-archive. As APK archive are supposed to contain their Android application icon, it becomes possible to display the application icon as the Nautilus thumbnail. You can also add APK version provided by the embedded manifest.xml.
This article explains all the steps needed to configure Nautilus to display the APK embedded application icon as thumbnail. This allows you to handle your APK files from Nautilus as they appear on your Android device.
This procedure has been tested under Ubuntu and Ubuntu Gnome 16.04 LTS and even LUbuntu with PCManFM.
It should be applicable to many other distributions.