This talk is based on a joint work in progress with Gurbir Dhillon. A remarkable theorem of Feigin and E. Frenkel from the early 90's describes the center of the universal enveloping algebra of an (untwisted) affine Kac-Moody Lie algebra at the so called critical level proving a conjecture of Drinfeld: the center in question is the algebra of polynomial functions on an infinite dimensional affine space known as the space of opers. In our work we study a part of the center in positive characteristic p at an arbitrary non-critical level. Namely, we prove that the loop group invariants in the completed universal enveloping algebra is still the algebra of polynomials on an infinite dimensional affine space that is ``p times smaller than the Feigin-Frenkel center''. In my talk I will introduce all necessary notions, state the result, explain examples and, time permitting, motivations.