I read this manga like 2 years ago. It is about a high school guy who receives a calling card of a cyborg, and then when he answers his phone, he is teleported to another dimension where everything is devastated and he starts to fight with monsters. He has a female friend with gray hair and glasses.


This sounds like it might be Psyren, though I don't remember any cyborgs in that manga. Synopsis from MAL:

Yoshina Ageha is a high school student who offers to help people with their problems for 10,000 yen. He'll take care of your stalkers, find your lost animal, whatever you want. One day when he's heading home, a nearby pay phone rings, and he picks it up. The only thing he hears however is his own voice echoing. After finding a mysterious card with the word 'Psyren' printed on it, his life suddenly changes as he is drawn into a crazy new world.

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