N. [. Achar, S. Cooney, and . Riche, The parabolic exotic t-structure, preprint

P. Achar, S. Makisumi, S. Riche, and G. Williamson, Modular perverse sheaves on flag varieties I: tilting and parity sheaves, AR2] P. Achar and S. Riche, Reductive groups, the loop Grassmannian, and the Springer resolution, pp.325-370, 2016.
DOI : 10.24033/asens.2284

URL : https://hal.archives-ouvertes.fr/hal-00937989

P. Achar and L. Rider, Parity sheaves on the affine Grassmannian and the Mirkovi?????Vilonen conjecture, Acta Mathematica, vol.215, issue.2, pp.183-216, 2015.
DOI : 10.1007/s11511-016-0132-6

[. Arinkin and D. Gaitsgory, Asymptotics of geometric Whittaker coefficients, available at http://www.math.harvard Perverse sheaves on affine flags and Langlands dual group (with an appendix by R. Bezrukavnikov and I. Mirkovi´cMirkovi´c), Israel J. Math, vol.170, pp.135-183, 2009.

. S. Abbgm, R. Arkhipov, A. Bezrukavnikov, D. Braverman, I. Gaitsgory et al., Modules over the small quantum group and semi-infinite flag manifold, Transform. Groups, vol.10, pp.279-362, 2005.

. Br-]-p, S. Baumann, and . Riche, Notes on the geometric Satake equivalence, preprint arXiv:1703.07288

R. Bezrukavnikov, D. Gaitsgory, I. Mirkovi´cmirkovi´-mirkovi´c, S. Riche, A. L. Rider et al., Analyse et topologie sur les espaces singuliers, I (Luminy, pp.5-172, 1981.

. A. Bgs, V. Be?-ilinson, W. Ginzburg, and . Soergel, Koszul duality patterns in representation theory, J. Amer. Math. Soc, vol.9, pp.473-527, 1996.

. J. Bl, V. Bernstein, and . Lunts, Equivariant sheaves and functors Bezrukavnikov, On two geometric realizations of an affine Hecke algebra, Lecture Notes in Mathematics Publ. Math. IHES, vol.1578, issue.123, pp.1-67, 1994.

R. Bezrukavnikov, A. Braverman, and I. Mirkovi´cmirkovi´c, Some results about geometric Whittaker model, Advances in Mathematics, vol.186, issue.1, pp.143-152, 2004.
DOI : 10.1016/j.aim.2003.07.011

URL : https://doi.org/10.1016/j.aim.2003.07.011

]. R. Ber, S. Bezrukavnikov, and . Riche, A topological approach to Soergel theory, in prepara- tion. [BY] R. Bezrukavnikov and Z. Yun, On Koszul duality for Kac?Moody groups, Represent . Theory, vol.17, pp.1-98, 2013.

. E. Cps, B. Cline, L. Parshall, and . Scott, Finite-dimensional algebras and highest weight categories, J. Reine Angew. Math, vol.391, pp.85-99, 1988.

]. G. Fa and . Faltings, Algebraic loop groups and moduli spaces of bundles, J. Eur. Math. Soc. (JEMS), vol.5, pp.41-68, 2003.

M. Finkelberg, I. Mirkovi´cmirkovi´cfk-]-e, R. Freitag, . Kiehl, T. Etale-cohomology et al., Semi-infinite flags I Case of global curve P 1 , in Differential topology, infinite-dimensional Lie algebras, and applications Amer Local geometric Langlands correspondence and affine Kac? Moody algebras, in Algebraic geometry and number theory, Frenkel, D. Gaitsgory, D. Kazhdan, and K. Vilonen, Geometric realization of Whittaker functions and the Langlands conjecture, pp.81-112, 1988.

D. [. Frenkel, K. Gaitsgory, and . Vilonen, Whittaker patterns in the geometry of moduli spaces of bundles on curves Ann, Math, vol.153, pp.699-748, 2001.

]. D. Ga and . Gaitsgory, Construction of central elements in the affine Hecke algebra via nearby cycles, Invent. Math, vol.144, pp.253-280, 2001.

]. J. Ja and . Jantzen, Representations of Algebraic Groups, second edition, Mathematical Surveys and Monographs 107 Modular representations of reductive groups and geometry of affine Grassmannians, Amer. Math. Soc, 2003.

D. Juteau, C. Mautner, G. Williamson, J. Parity-sheaves, and . Amer, Math. Soc, vol.27, pp.1169-1212, 2014.

D. Juteau, C. Mautner, and G. Williamson, Parity sheaves and tilting modules, Annales scientifiques de l'??cole normale sup??rieure, vol.49, issue.2, pp.257-275, 2016.
DOI : 10.24033/asens.2282

]. G. Lu, . Lusztig, ]. O. Singularitiesma, and . Mathieu, Analysis and topology on singular spaces, II, III (Luminy Filtrations of G-modules, Soc. Math. FranceMR] C. Mautner and S. Riche, Exotic tilting sheaves, parity sheaves on affine Grassmannians , and the Mirkovi´cMirkovi´c?Vilonen conjecture, preprint arXiv:1501.07369, to appear in J. Eur. Math. Soc. [MV] I. Mirkovi´cMirkovi´c and K. Vilonen, Geometric Langlands duality and representations of algebraic groups over commutative rings, Ann. of Math, pp.208-229, 1981.

]. D. Na and . Nadler, Perverse sheaves on real loop Grassmannians, Invent. Math, vol.159, pp.1-73, 2005.

. C. Np-]-b, P. Ngô, and . Polo, Résolutions de Demazure affines et formule de Casselman? Shalika géométrique, J. Algebraic Geom, vol.10, pp.515-547, 2001.

]. S. Ri and . Riche, Geometric Representation Theory in positive characteristic, habilitation thesis , available on https

W. [. Riche, G. Soergel, and . Williamson, Abstract, Compositio Mathematica, vol.27, issue.02, pp.273-332, 2014.
DOI : 10.1007/BFb0078365

G. [. Riche and . Williamson, Tilting modules and the p-canonical basis, Astérisque, vol.397, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01249796

, Quelques applications de la cohomologie d'intersection, Exp. 589, pp.92-93, 1981.

]. J. Wa and . Wang, A new Fourier transform, Math. Res. Lett, vol.22, pp.1541-1562, 2015.

, E-mail address: bezrukav@math.mit E-mail address: gaitsgde@math.harvard E-mail address: mirkovic@math.umass E-mail address: simon.riche@uca E-mail address: laurajoy@uga