On a M104 3.2L what is the last pump on the left...?
 

It is the last pump on the serpentine belt - farthest on the passenger side. This pump is making 'hollow', kind of 'whirring' noise especially when cold. What is it? How much does one cost? Is it the air pump?

Assuming "left" staring at the engine...you would be looking at the air pump.

It's only doing it's job in the first few minutes after startup, pumping air into the system to hasten cat warmup so that optimum emissions efficiency can occur quickly. In Europe, the sniffer gets inserted and data analyzed within the first 60 seconds of startup...a far more stringent test than in the US.

In fact, it probably isn't needed for US emissions, except that the missing component would fail the visual portion of the inspection.

When the air pump get old, the most common failure is that the clutch bearings wear out and seize. I believe kits are now available to replace just that, rather than the whole $800+ unit. The bearing are a weird size and can't be procured easily.

Thanks. Great explanation. I called the dealer and asked about the air pump cost and was shocked at the price. Looks like I'll need one in the near future. I also have a code 26 fault which is the 2-3 upshift delay to warm up the cat. I am assuming thatthis fault is not related to this failure?

That "hollow, whirring" noise is not indicative of a failure (mine does that too)...a screeching noise IS!

And the air pump has nothing to do with the upshift delay...as I stated earlier, it does its job pretty early upon startup, then ceases.

You can get just the pulley kit for your air pump 104-140-08-86,pump usually OK.pulley bearing is cause problem.