NOVELTY - Fractionating cellulosic biomass into cellulose, hemicellulose, and lignin, comprises: providing a feedstock comprising lignocellulosic biomass; in a digestor, fractionating feedstock under effective fractionation conditions in the presence of a solvent for lignin, carbon dioxide, and water, to produce a liquor containing hemicellulose, cellulose-rich solids, and lignin; removing cellulose-rich solids from liquor; hydrolyzing hemicellulose contained in liquor, under effective hydrolysis conditions, to produce hemicellulosic monomers; recovering hemicellulosic monomers; and recovering lignin.    USE - The process is useful for fractionating cellulosic biomass into cellulose, hemicellulose, and lignin (claimed) which are useful to produce biochemicals or biofuels e.g. ethanol and acetone.    ADVANTAGE - The process: is flexible, thus enabling multiple uses for the products; and produces cellulose-rich solids while concurrently producing a liquid phase containing a high yield of both hemicellulose sugars and lignin, and low quantities of lignin and hemicellulose degradation products.    DETAILED DESCRIPTION - Fractionating cellulosic biomass into cellulose, hemicellulose, and lignin, comprises: (a) providing a feedstock comprising lignocellulosic biomass; (b) in a digestor, fractionating the feedstock under effective fractionation conditions in the presence of a solvent for lignin, carbon dioxide, and water, or in the presence of a solvent for lignin, carbonic acid and water, or in the presence of a solvent for lignin, water, and a carbonate dianion or its salt and/or a bicarbonate anion or its salt, to produce a liquor containing hemicellulose, cellulose-rich solids, and lignin; (c) removing the cellulose-rich solids from the liquor; (d) hydrolyzing the hemicellulose contained in the liquor, under effective hydrolysis conditions, to produce hemicellulosic monomers; (e) optionally hydrolyzing at least some of the cellulose-rich solids to produce glucose; (f) optionally recovering at least some of the cellulose-rich solids as a cellulose product; (g) recovering the hemicellulosic monomers, and optionally the glucose if step (e) is conducted, to produce fermentable sugars; and (h) recovering the lignin.