One of the most commonly asked question in wireless domain is-

“In Centralized architecture what is the function of AP?”
OR
“What information is stored on AP (as thin client in Centralized architecture) and what else on WLC”?

This is what a LAP (Lightweight Access Point/Thin AP) does-

Real-Time 802.11/MAC Functionality:
• Beacon Generation
• Probe Response
• Power management/Packet buffering
• 802.11e/WMM scheduling, queueing
• MAC layer data encryption/decryption
• 802.11 control messages
•Data Encapsulation/De-Encapsulation
•Translational Bridging (H-REAP Local Switching)
•Fragmentation/De-Fragmentation

And Rest is done by WLC which includes (not limited to)-

Non Real-Time 802.11/MAC Functionality:
• Association/Disassociation/Reassociation requests/response
• 802.11e/WMM (Wi-fi Multimedia)
• 802.1X/EAP (Port based authentication)
• Key management
•802.11 Distribution Services
•802.11 STA (Client/Station) Services (Auth/Deauth/Privacy)
•Wired/Wireless Integration Services