  In this paper, we give a concrete description of the two-fold cover of a
simply connected, split real reductive group and its maximal compact subgroup
as Chevalley groups. We define a representation of the maximal compact subgroup
called pseudospherical representation, it appears with multiplicity one in the
principal series representation. We introduce a family of canonically defined
intertwining operators and compute the action of them on pseudospherical
K-types, obtaining explicit formulas of the Harish-Chandra c-function.
