what oil for the rear diff?

Royal Purple or Redline, Both are the best in the states, They even include additives for LSD Diffs!

I agree with ///MTurbo and here in the UK I always use the Redline products in vehicles once the warranty has expired.
I use it in both transmissions and differentials but am happy with Castrol for my engines. Redline is also available for engines but I have had no call to use it so cannot make a justified opinion.

8Tech.

If you have an LSD, then you should use Castrol SAF-XJ synthetic, which was specially developed with BMW. However, as standard, the 840 does not have an LSD, so other oils, such as those by Royal Purple, would be suitable.

http://www.castrol.com/castrol…mepage.do?categoryId=3205

We stock the Morris range of oils and I'd go for the XFS (extreme fully synthetic) 80W/140 LSD differential oil every time.
We supply Vauxhall for use in the Monaro race cars as well as TVR Tuscan racers and the like, it's good stuff and at a little over thirty quid a gallon is pretty reasonable compared to the bigger name brands.
As for Red Line, it's kind of like Marmite, people seem to love it or hate it, I work at a gearbox builders and have seen the damage this stuff can do when it overheats and starts blocking oilways and cooking synchros so couldn't recomend it (unless you've tried everything else and still have problems).
I believe there's an article floating about on the web slagging it off (it was posted on one of the Ford forums some time back) explaning in some detail why it doesn't work, what made it interesting reading was the fact that was allegedly written by the guy that originaly designed the stuff.
Disgruntled ex company employee? don't know, but worth a read anyway.

I had my 3.91 diff fitted today, I got the oil from BMW £23 for 2ltrs, (take your own 2ltr bottle as they use the large drums)