Let F be a p-field. Let E∕F
be a tamely ramified cyclic extension of odd degree. Denote by πE∕F and Π
respectively, the lift and the Shintani lift of an irreducible supercuspidal
representation π of Gl2(F). The comparison of these two lifts of π is made by
breaking up the formula for the character of a supercuspidal representation into a
sum over a certain set of double cosets. As a result, we show that the liftings πE∕F
and Π are equivalent.