take Nexus 7 from android 4.3 to 4.2.2 I have just purchased a Nexus 7 (2013) and it auto updated to android to 4.3 as I was setting up.
Unfortunately USB OTG now does not run.  I purchased the Nexus 7 for it's OTG feature.
I've done a factory reset but it still loads 4.3 
Is there any way I can go back to 4.2.2 - which does support OTG on the Nexus 7
I don't think the Nexus 7 (2013) ever had Android 4.2. I was going to suggest flashing a factory image but the only one available is Android 4.3 which suggests it's not possible.

As the other answers have suggested you will probably need to root to get the USB OTG functionality you are after.