  We generalize the construction of M. Lieblich for the compactification of the
moduli stack of $\PGL_r$-bundles on algebraic spaces to the moduli stack of
Tanaka-Thomas $\PGL_r$-Higgs bundles on algebraic schemes. The method we use is
the moduli stack of Higgs version of Azumaya algebras. In the case of smooth
surfaces, we obtain a virtual fundamental class on the moduli stack of
$\PGL_r$-Higgs bundles. An application to the Vafa-Witten invariants is
discussed.
