The BenQ W4000i user manual mentions that projector has both an HDMI-eARC and Optical Output so it should connect to any of the Sonos HT products. It’s just a case of running a chosen cable from the Projector to the Soundbar. I can’t see any reason for why the Projector would be incompatible? It all looks compatible to me.

Thx for your reply.

just to be thorough, i understand I’ll have to do the setup like this :

Internet (RJ45) -> apple tv (hdmi) → BenQw4000i (hdmi) → Sonos ARC (Bluetooth) → Sonos Sub and Sonos ERA.

Am I correct ? Why would the optical output be of use ? 
thx A LOT for your help.

I would perhaps cable the Sonos Arc to the eARC (enhanced Audio Return Channel) port of your Projector instead. - the Optical connection is just an alternative way to get the audio out to the Arc (using the Sonos Optical Adapter supplied with the Sonos Arc).

Important note: the Sonos Arc does not have a Bluetooth Rx.

Then wifi ?

how does the Sonos Arc communicate with the sub and era ? Wireless or with wire ? 
 

thank you :-)

Over their built-in 5Ghz WiFi adapters - the communicating is an ad-hoc wireless connection between the players themselves.