The Eye Of Tyr in Norse mythology is the eye of the god of war Tyr, now pardon me if I don't get into the whole BDK story, but if someone else can explain it better you should really ask about it as it is an interesting story with lots of tie ins to many other feuds in Chikara, Wikipedia will also be stolen hugely from
In Chikara however, is a mysterious Scandinavian artifact that can be used to control people's minds, but had gone missing from Switzerland, a guy named Dr. Cube had come in possession of it, and wanted Chris Hero to come wrestle for him since he was a fan of Hero, UltraMantis Black wanted the Eye Of Tyr, made a deal with Hero, that if he could get him the counter for the Chikara Special (a move invented by Mike Quackenbush that had caused here quite the trouble throughout 2007) Hero would go wrestle for Dr. Cube, Mantis taught the move to Hero, and in favor Hero left Chikara and went to wrestle for Cube.
In 2009 Mantis revealed all this and revealed that he had the Eye Of Tyr, and he wanted a 3rd member of The Order of the Neo-Solar, having failed with attemps such as Pinkie Sanchez & Sami Callihan, Mantis used the Eye Of Tyr to gain control of Delirious to get back at Delirious's tag partner Hallowicked, to make him the 3rd member, now here comes a part that'll play into the whole BDK story, because cccording to legend, once the Eye is used, it must be given away, or the user would face bad luck and tragedy. However, UltraMantis didn't believe this and refused to let go of the Eye.
During the third night of the 2009 Young Lions Cup, a man dressed in a white mask and clothes confronted UltraMantis Black in the ring and gave him a box. Inside of the box was a message stating that a war was coming. That same man would then begin sending messages over the internet to UltraMantis saying that he and his Temple would be destroyed if he did not return the Eye of Tyr to the "family". At Cibernetico Increible the man was joined by another larger man dressed in similar fashion and together they appeared in the crowd and confronted UltraMantis, who proceeded to flee the arena. Following the event a cyborg named Vökoder, who had debuted during the Young Lions Cup, came to UltraMantis and offered to protect the Eye of Tyr and to convince him of his sincerity, Vökoder started interfering in UltraMantis' matches in order to help him win. Eventually, UltraMantis made Vökoder the fourth member of The Order of the Neo–Solar Temple.
At the conclusion of the season eight finale titled Three-Fisted Tales, the two masked men once again confronted UltraMantis, calling him the man with the real power in Chikara. This time both men removed their masks and revealed themselves as Ares and Tursas. Immediately following this, Vökoder, who had been given the Eye of Tyr for safekeeping, attacked UltraMantis, while Claudio Castagnoli, Carpenter Ant, Sara Del Rey and Daizee Haze all turned rudo and helped Ares and Tursas beat down the tecnicos, who had gathered around the ringside area. Once the fight had subdued with the new group on top, Carpenter Ant unmasked as Pinkie Sanchez and Vökoder unmasked as Tim Donst, both of whom had a history with UltraMantis Black. After a salute, the group fled the arena with the Eye of Tyr intact.
On February 28, 2010, at A World of Comforting Illusions UltraMantis Black and Delirious used their three points and challenged The Colony of Fire Ant and Soldier Ant for the Campeonatos de Parejas. The Colony retained their titles in two straight falls, after Ares came out and used the Eye of Tyr to release Delirious, who then proceeded to go crazy and run out of the arena, abandoning UltraMantis. The following day Ares declared victory over UltraMantis and announced that now that he had gained revenge on him by destroying his dream of winning, not only the Campeonatos de Parejas, but also the King of Trios, he would be returning the Eye of Tyr to Switzerland and his father's collection.
In the end of 2011 UltraMantis sought to end his long rivalry with Ares by challenging him to a match at Chikara's first ever Internet pay-per-view, offering to put his mask on the line against Ares' Eye of Tyr. On November 13 at High Noon, UltraMantis and Hallowicked defeated Ares and Tim Donst in a No Disqualification match with UltraMantis pinning Ares to regain the Eye of Tyr. In winning the match, UltraMantis and Hallowicked also picked up their third point, earning the right to challenge for the Campeonatos de Parejas. UltraMantis first used the Eye of Tyr to get rid of Sinn Bodhi, handing him what was later revealed as a fake replica, which led to Bodhi parting ways with the promotion.
By all means, someone should really explain this better as I am horrible at stuff like this and my knowledge is pretty holed and mostly filled out by wiki, but I did it as well as I could