OEM XR500R 81/82
As soon as I got my first XR500R, back in 1981, I realized that its exhaust header was of a smaller diameter than the one on the XR500 79/80. No need to say, I was disappointed. There must have been a good reason for that (probably something to do with the reed valve inlet) for my, bigger had to be better. Fast forward  several decades and it now has a XR500 header.

Me in 1982 on a XR500R 1981
Original header on a XR500R 1981

The XL500R was fitted again with larger diameter pipes (and an additional heat shield to protect the clutch and automatic decompressor cables).

In 1980, the racing wisdom was that a tricked XR500 would benefit from not only bigger pipes but header pipes of the same length and volume. Al Baker got Mugen to build a header that would be commercialized and fitted to the racing bikes of the day, from the Baja to the Paris Dakar.

Jacky Barat XR550R Paris Dakar 1983
1982 XR550R of Jacky Barat at the Paris Dakar 1983, with the Mugen header

Providers of aftermarket exhausts obviously also got in the game.

Protec exhaust header for XR500
Out of the box

Protec exhaust header for XR500
Pro-tec in business

The stock heat shield can be fitted onto the Protec

I am a little fuzzy on the Supertrapp. No definitive proof. If you know, please share.

Supertrapp on a XR500R?
I think this one is Supertrapp

I know this one is Supertrapp, but it does not quite fit a XR/XLS500 (79-80) or XR500R (81-82 even 83-84)

NOS Supertrapp, does not quite fit the XR500
NOS but does not quite fit