What is 'awesomium_process.exe'?
Solution 1:
The awesomium_process.exe
is a lightweight web browser based on Webkit, that is used by several games (including Guild Wars 2 and Lord of the Rings Online). In Guild Wars 2 specifically, it is used for the Black Lion trading post screens (Gem Store, Currency Exchange, Trading Post, etc).
Killing the process will result in the process being relaunched the next time you visit any of these screens. Preventing the process from running at all will result in these screens simply not working anymore.
Deleting the executable will result in it being recreated the next time the game is started.
The official website for Awesomium is awesomium.com.
A discussion on Guild Wars 2 Guru regarding this process can be found here.