The air pump system only functions when starting from cold.
Some people here have had this problem occur with a leaky air pump and had it replaced under warranty. However there are a few things that can cause the 410 code, but it is usually when the air pump fails to pull enough current by either not switching on or running without load. It only actually operates for about a minute when you start the engine from cold to inject air into the exhaust manifold to heat up the cats, after that it does nothing!

The air pump relay supplies power to the pump when required so could well be the problem, It is actually inside the relay control module and not a discrete item.

The part No. I believe is: 5099 007AA, see below:



To save money Bosch has mounted a row of open-frame relays on a PCB rather than use individual relays. You can pop the module open and have a look at the relays to check that they are move freely and the contacts are good. Also check that there are no hairline cracks on where the terminals are soldered to the PCB. See below: