The Orbit Method and Character Formulas for Tempered representations of a Nonconnected Reductive Real Algebraic Group

Let G be a possibly disconnected reductive real Lie group. In this paper, I parametrize the set of irreductible tempered characters of G. I then describe these characters using certain Kirillov's formulas,'' based on the descent method near each elliptic element in G. If G is linear and connected, the parameters I use are final basic’’ parameters in the sense of Knapp and Zuckerman.