The application processor could be anything; from an 8-bit micro up to a PC.
Also check out Anaren's Zigbee module:
http://www.anaren.com/air/products/air-for-zigbee-standard-apps
It's ZNP based and has a ton (over 30!) of very cool examples. They have hardware development kits, reference designs, and software that works with both MSP430 and Stellaris. It's also been successfully ported to a plethora of MSP430s, Stellaris 3S & 4F families, Microchip's PIC, and Linux. Let me know offline if you would like a dev kit for it.
Regards,
Derek