Tight closure/localization problem/description

Let  ${}S\subseteq R$  be a multiplicative system and ${}I$ an ideal in ${}R$. Then the localization problem of tight closure is the question whether the identity

${}(I^{*})_{S}=(IR_{S})^{*}\,$

holds.

Here the inclusion ${}\subseteq$ is always true and ${}\supseteq$ is the problem. The problem means explicitly:

if  ${}f\in (IR_{S})^{*}$,  can we find an  ${}h\in S$  such that  ${}hf\in I^{*}$  holds in ${}R$?