Process for the preparation of a polyurethane prepolymer having (2-oxo-1,3-dioxolan-4-yl)methyl carbamate end groups comprising: - in a first stage (denoted E1), the preparation of a polyurethane prepolymer having NCO end groups by a polyaddition reaction: (i) of at least one diisocyanate chosen from the following aliphatic or aromatic diisocyanates, and their mixtures: a1) isophorone diisocyanate (IPDI), a2) toluene-2,4-diisocyanate (2,4-TDI), a3) diphenylmethane-2,4'-diisocyanate (2,4'-MDI), (ii) with at least one polyol chosen from polyether polyols and polydiene polyols, at a reaction temperature T1 of less than 95°C, under anhydrous conditions and in amounts of diisocyanate(s) and of polyol(s) resulting in an NCO/OH molar ratio, denoted r 1, ranging from 1.6 to 1.9; then - in a second stage (denoted E2), the reaction, under anhydrous conditions, at a reaction temperature T2 of less than 95°C, of the product formed in the first stage E1 with at least one glycerol carbonate in an amount of glycerol carbonate resulting in an NCO/OH molar ratio, denoted r 2, ranging from 0.9 to 1.0, - it being possible for the toluene-2,4-diisocyanate (2,4-TDI) to be used in the form of a TDI mixture a2) comprising at least 99% by weight of toluene-2,4-diisocyanate (2,4-TDI), with respect to the total weight of said mixture a2), and - it being possible for the diphenylmethane-2,4'-diisocyanate (2,4'-MDI) to be used in the form of an MDI mixture a3) comprising at least 99% by weight of diphenylmethane-2,4'-diisocyanate (2,4'-MDI), with respect to the total weight of said mixture a3). - in a first stage (denoted E1), the preparation of a polyurethane prepolymer having NCO end groups by a polyaddition reaction: (i) of at least one diisocyanate chosen from the following aliphatic or aromatic diisocyanates, and their mixtures: a1) isophorone diisocyanate (IPDI), a2) toluene-2,4-diisocyanate (2,4-TDI), a3) diphenylmethane-2,4'-diisocyanate (2,4'-MDI), (ii) with at least one polyol chosen from polyether polyols and polydiene polyols, at a reaction temperature T1 of less than 95°C, under anhydrous conditions and in amounts of diisocyanate(s) and of polyol(s) resulting in an NCO/OH molar ratio, denoted r 1, ranging from 1.6 to 1.9; then (i) of at least one diisocyanate chosen from the following aliphatic or aromatic diisocyanates, and their mixtures: a1) isophorone diisocyanate (IPDI), a2) toluene-2,4-diisocyanate (2,4-TDI), a3) diphenylmethane-2,4'-diisocyanate (2,4'-MDI), a1) isophorone diisocyanate (IPDI), a2) toluene-2,4-diisocyanate (2,4-TDI), a3) diphenylmethane-2,4'-diisocyanate (2,4'-MDI), (ii) with at least one polyol chosen from polyether polyols and polydiene polyols, at a reaction temperature T1 of less than 95°C, under anhydrous conditions and in amounts of diisocyanate(s) and of polyol(s) resulting in an NCO/OH molar ratio, denoted r 1, ranging from 1.6 to 1.9; then - in a second stage (denoted E2), the reaction, under anhydrous conditions, at a reaction temperature T2 of less than 95°C, of the product formed in the first stage E1 with at least one glycerol carbonate in an amount of glycerol carbonate resulting in an NCO/OH molar ratio, denoted r 2, ranging from 0.9 to 1.0, - it being possible for the toluene-2,4-diisocyanate (2,4-TDI) to be used in the form of a TDI mixture a2) comprising at least 99% by weight of toluene-2,4-diisocyanate (2,4-TDI), with respect to the total weight of said mixture a2), and - it being possible for the diphenylmethane-2,4'-diisocyanate (2,4'-MDI) to be used in the form of an MDI mixture a3) comprising at least 99% by weight of diphenylmethane-2,4'-diisocyanate (2,4'-MDI), with respect to the total weight of said mixture a3).