wirelessly connecting apple tv to projector

The Apple TV requires a physical connection, which is done via HDMI. You cannot set it up wirelessly.

Once you have the Apple TV setup you can use airplay to wirelessly stream content from your local iTunes library, or compatible videos from safari, as well as mirroring your Mac's display.

How to AirPlay video and mirror your device's screen to Apple TV - Apple Support

Why do you need to connect the Mac to the ATV to the projector? Is there a reason that you can't just connect the Mac to the projector? What, exactly, are you trying to accomplish? The more details you provide, the better the answers you'll get.

It would also be helpful if you said which Mac and what type of projector.

Writing an effective Apple Support Commun… - Apple Community