 
Summary: COMPOSITIO MATHEMATICA, Vol. 40, Fasc. 1, 1980, pag. 87121
© 1980 Sijthoff & Noordhoff International Publishers  Alphen aan den Rijn
Printed in the Netherlands
A TRACE FORMULA FOR REDUCTIVE GROUPS II:
APPLICATIONS OF A TRUNCATION OPERATOR
James Arthur*
1. A truncation operator ............. 89
2. Integrability of k(x,) ............ 98
3. The operator Mp(7r) .... .. 107
4. Evaluation in a special case . .......... 113
5. Conclusion . ................ 120
Introduction
This paper, as promised in the introduction to [l(c)], contains an
identity which is valid for any reductive group G over 0, and which
generalizes the Selberg trace formula for anisotropic G. We have
already shown that a certain sum of distributions on G(A)', indexed
by equivalence classes in G(Q), equals the integral of the function
E kT(X,f), x E G(Q)\G(A)1.xEt
The main task of this paper is to show that the integral may be taken
inside the sum over X. There does not seem to be any easy way to do
