in the local langlands program the (smooth) representation theory of p-adic reductive groups g in characteristic zero plays a key role. for any compact open subgroup k of g there is a so called hecke algebra $h(g,k)$. the representation theory of g is equivalent to the module theories over all these algebras $h(g,k)$. very important examples of such subgroups k are the iwahori subgroup i and the pro-p iwahori subgroup $i_p$. by a theorem of bernstein the hecke algebras of these subgroups (and many others) have finite global dimension. in recent years the same representation theory of g but over an algebraically closed field of characteristic p has become more and more important. but little is known yet. again one can define analogous hecke algebras. their relation to the representation theory of g is still very mysterious. moreover they are no longer of finite global dimension. in joint work with r. ollivier we prove that the characteristic p version of $h(g,i_p)$ is gorenstein.