Аннотация:A description of the algebra of outer derivations of a group algebra of a
finitely presented discrete group is given in terms of the Cayley complex of the
groupoid of the adjoint action of the group. This task is a smooth version of
Johnson’s problem concerning the derivations of a group algebra. It is shown
that the algebra of outer derivations is isomorphic to the group of the one-
dimensional cohomology with compact supports of the Cayley complex over the
field of complex numbers.