  We extend the standard construction of the adjoint representation of a Lie
groupoid to the case of an arbitrary higher Lie groupoid. As for a Lie
groupoid, the adjoint representation of a higher Lie groupoid turns out to be a
representation up to homotopy which is well defined up to isomorphism. Its
existence and uniqueness are immediate consequences of a more general result in
the theory of simplicial vector bundles: the representation up to homotopy
obtained by splitting a higher vector bundle by means of a cleavage is, to
within isomorphism, independent of the choice of the cleavage.
