Also the behavior is different when it’s just after a restart of the phone or later.
After a fresh restart, the Google Play store will start the download of the APK (according to the downloaded size), then will get stuck for a moment, then it will download the OBB. After the completion of the download, it will say that the app failed to install (but it will still appear in the list of apps).
If I retry a new installation of the app just after, the download will start and run without any problem. But when it’s finished, the OBB is not installed and the app is not working.
I would suspect a problem with my phone, but actually I have a co-worker who is using another phone and who has the same problem with the app, so I’m starting to think that it may be a bug of UE4.