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English speakers might talk about a "phase", but thanks to the Internet, the Japanese term has started to catch on in English, and some translations of Japanese works (such as Love, Chunibyo & Other Delusions!) will leave the term untranslated. While chuunibyou is by no means limited to Japan, in the grand tradition of Japanese Media Tropes, Japan is the first country to give the phenomenon a name (partly by having a particularly weird twist to it). This subtype had its own Trope Codifier in the popular Boogiepop light novel series, which starts a main character with a superpowered split personality that only differentiates itself by wearing a costume and talking in a cooler way.
They often create a persona with an Awesome McCoolname or Atrocious Alias (there's almost no middle ground) to display these magical abilities. These guys are Sham Supernaturals who believe they have Magic and Powers and will try to convince others that their powers are real (stereotypically a Magical Eye under a surgical eyepatch, or an Evil Hand which they grasp in supposed pain).
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