Where does Google Play Store put downloaded apps? I want to know where Google Play stores downloaded .apk files. I've heard that Google Play doesn't send you an .apk file and installation is completely online. Is it true?
.apk files are downloaded and stored in subfolders under a location on your device called /data.

By default, you do not have permissions to read from that location. In order to read/write in that location, you will need to root your device.