  This paper introduces the proper notion of variational quasiconvexity
associated to a group of diffeomorphisms. We prove a lower semicontinuity
theorem connected to this notion. In the second part of the paper we apply this
result to a class of functions introduced in [5]. Such functions are
$GL(n,R)^{+}$ quasiconvex, hence they induce lower semicontinuous integrals.
