In Times Square, amid the dozens of Elmos, Mickey Mouses and superheroes who work the crowds for loose bills, new costumed characters have come to seek their fortunes.

They are mostly men of Chinese descent, with shaved heads, beatific smiles and flowing robes of orange, but sometimes brown or gray. They follow a similar script: Offering wishes of peace and a shiny amulet, they solicit donations from passers-by, often reinforcing their pitch by showing a picture of a temple for which the money seems to be intended. Then they open a notebook filled with the names of previous donors and the amounts given.

The men appear to be Buddhist monks; a smaller number of similarly dressed women say they are Taoist nuns.

No one seems to know who they really are or where they come from. The police have taken no official stance, stepping in only when the monks become aggressive. Various Buddhists have confronted the men, asking about their affiliation or quizzing them about the religion’s precepts. The men remain silent or simply walk away.