It could be that you are using inferior parts, I went through that a while back! Maybe do a search of my posts if you are interested. Do you have any more info on exactly what the "split air" code is referring to ??

For sure there should be no exhaust going back through the air valve, that can ruin the air pump and the flow sensor.

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1988 325is (purchased new) sold
2004 X5 3.0 2005 X3 2.5
2008 X5 3.0 (new to me)