Friction in newly installed bottom bracket I could do with some help on a bike build... 

I've installed a BB86/92 Trivatuv pressfit GXP bottom onto my Production Privee Shan frame. I used a headset press and everything seemed to go smoothly.

When I insert the crank (SRAM X1) I can hear what sounds like a small amount of friction/rubbing between the spindle and the BB as I turn it. When I tighten the cranks they doesn't spin very freely, maybe 1 or 2 turns.

Finally after fitting the chain, I can't shift into the easiest gear. When I try the friction between the crank and the bottom bracket increases. If I try very hard to change up I can make it so I can't spin the cranks at all.

My best guess is that the bottom bracket is slightly misaligned and when I try to shift into the easiest gear the lateral tension on the crank is causing lots of friction between the spindle and the sleeve of the bottom bracket.

Any suggestions?
Sounds like a spacing issue, the cranks shouldn't bind at all.  They may have some resistance with new bearings, but not enough to noticeably feel in most cases. Check that you don't have excess spacers on the spindle and are just using the wavy washer.  

The crank arm bolt should pretty much bottom out on install and the cranks should be easy to turn. (there is a black alloy spacer that is used for BB86 shells included with most SRAM gxp cranks/bb and is not needed on the BB92 install).

If that looks correct, have a visual check in the BB.  It uses a plastic shell and sometimes this can be damaged when pressing in and contact the crank spindle on install.  Next check that the bearing cups are not deformed where they meet the frame on the outside (ie pressed in too hard) which can cause the bearings to run out of alignment, again a plastic shell issue and can happen when using larger headset presses.

Worst case, replace the BB with something like a Wheels Manufacturing or Hope BB that use alloy parts throughout; these are much more reliable for press fit applications as they do not deform like the plastic ones.