  Let G be the group GL(N,F), where F is a non-archimedean locally compact
field. Using Bushnell and Kutzko's simple types, as well as an original idea of
Henniart's, we construct explicit pseudo-coefficients for the discrete series
representations of G. As an application we deduce new formulas for the value of
the Harish-Chandra character of certain such representations at certain
elliptic regular elements.
