  Using generalized Blumenthal--Getoor indices, we obtain criteria for the
finiteness of the $p$-variation of L\'evy-type processes. This class of
stochastic processes includes solutions of Skorokhod-type stochastic
differential equations (SDEs), certain Feller processes and solutions of L\'evy
driven SDEs. The class of processes is wider than in earlier contributions and
using fine continuity we are able to handle general measurable subsets of $R^d$
as state spaces. Furthermore, in contrast to previous contributions on the
subject, we introduce a local index in order to complement the upper index.
This local index yields a sufficient condition for the infiniteness of the
$p$-variation. We discuss various examples in order to demonstrate the
applicability of the method.
