Hamazaki Tatsuya manga
Tsurugi Tatsuno is a boy who competes in Virtual Digimon Battle tournaments. When a Kuwagamon appeared in the Real World, his Greymon came to life and protected him. Tsurugi is summoned to the Digital World by Piximon to save the Digital World from the evil Barbamon. Since his Digimon has a hexagon shape on him, it's an Illegal Digimon, meaning that Digimon bearing such symbols can help save the Digital World. Tsurugi's Greymon later De-Digivolves to Agumon and they meet other characters destined to save the Digital World from the forces of Barbamon. Now they must stop Barbamon and his minions before they get all the DigiMemories and take over both worlds.
From Tokyopop: Welcome to The World, the most advanced online game ever created. In The World you can be anyone you want to be, act out your adventure fantasies and through teamwork and determination, you can even become a hero. 14-year-old twins Shugo and Rena just won a contest that lets them play as the legendary avatars 'Kite' and 'Black Rose.' Armed with the power of the Twilight Bracelet, the two must discover what is causing rogue monsters to infect The World and carry on the legend of the .hackers.
It is the year 2017, and the stakes have gotten even higher in the massively multiplayer online game The World--now The World R:2, a dangerous place overrun by player killers, where lawlessness abounds. The PKK Haseo, known as "The Terror of Death," is a fearsome foe who punishes those who want to slay other players. But things have gotten personal as Haseo tries to track down the killer Tri-Edge, who has threatened the real life of his friend Shino... ~Summary by Tokyopop