Accel World

No matter how much the times change, bullied kids aren't going anywhere. And fat junior high school student Haruyuki is one of them. But one day, Haruyuki encounters Kuroyukihime, the most beautiful and elegant girl at school, who gives him a mysterious program: "Brain Burst"...and the secret of the "Accelerated World." He may be at the bottom of the food chain at school, but Haruyuki and his destiny begin to "accelerate" with incredible speed in the virtual realm as he aims for the top!! The manga adaptation of Reki Kawahara's wildly popular Accel World light novel series follows in the footsteps of its predecessor, bringing you a futuristic coming-of-age tale about the potential that lies within all of us! 

(Source: Yen Press)

Chiaki recently returned from America, enrolling into an all-girls school. Her brother used to tell her stories about a "Snow Black Princess" and her adventures in a magical kingdom before he died. Seeing an opportunity, two of her seniors try to install Brain Burst on her, only to be rejected. Turns out her brother already installed it three years ago on his deathbed, and is an unknowing Avatar.

(Source: TV Tropes)