A cross-polymer comprising a recurring unit of formula below: or its salt, solvate or isomer, wherein: PLS is a radical of a polysaccharide; PLS-RU is a radical of a repeating unit of the polysaccharide; PAA is a radical of a polyamino acid, wherein the polyamino acid is selected from the group consisting of a homo-, a random and a block co-polyamino acid, with the proviso that the homo-polyamino acid is not polycationic; AA is a radical of an amino acid unit of the polyamino acid; subscript x of the radical is an integer ranging from 1 to 200; subscript v of the radical [ - x] is an integer ranging from 1 to 48; subscript w of the radical (PLS-RU) is an integer ranging from 1 to 200; In is a ROP initiator which comprises a terminal X group per each [ -] radical, wherein each terminal X group is directly bond to each [ -] radical, and wherein the terminal X group is selected form the group consisting of -NH-, -O-, -S-, or combinations thereof; CL is a radical selected from the group consisting of: (C 1 -C 500)-alkyl, wherein two or more H are substituted by: (C 1 -C 500)-alkyl; (C 3 -C 30)-cycloalkyl, C-radical derived from a ring system with 1-6 rings, each ring being independently saturated, partially unsaturated or aromatic, the rings of the ring system being isolated or fused and each ring having 3-20 elements each element independently selected from the group consisting of C, CH, CH 2, CO, O, S, N and NH, OH, NR a R b, ONR c R d, CN, halide, SH 2, SR e R f, N NH 2, R g COR h, COOR i, CON(R j)(R k), R l N(R m)CON(R n)(R' n), (C 1 -C 30)-alkene, (C 1 -C 30)-alkyne, N 3, R o CH(OR p)(OR q), R r CH(SR s)(SR t), R u B(OR v)(OR w), COR x; and wherein none, one of more C, are independently replaced by (C 3 -C 30)-cycloalkyl, aryl, aryl-(C 1 -C 30)-alkyl, NR y R z, CO, O, S, S, S(O 2), B, P and (O-CH 2 -CH 2) A; subscript A of the radical (O-CH 2 -CH 2) is an integer number between 1 and 500; R a, R b, R c, R d, R e, R f, R h, R i, R j, R k, R m, R n, R' n, R p, R q, R s, R t, R v, R w, R x, R y and R z are radicals independently selected from the group consisting of H, (C 1 -C 30)-alkyl, (C 1 -C 30)-alkylphenyl, phenyl-(C 1 -C 30)-alkyl, and (C 3 -C 8)-cycloalkyl; wherein, in any of them, except for H, one or more carbons are optionally substituted by a heteroatom selected from the group consisting of O, S, S, S(O 2), halide, N, NH, P, and CO; R g, R l, R o, R r and R u are radicals independently selected from the group consisting of (C 1 -C 30)-alkyl, (C 1 -C 30)-alkylphenyl, phenyl-(C 1 -C 30)-alkyl, and (C 3 -C 8)-cycloalkyl; wherein, one or more carbons are optionally substituted by a heteroatom selected from the group consisting of O, S, S, S(O 2), halide, N, NH, P, and CO; with the proviso that: CL may be present or not, so that if CL is not present, the PLS-RU radical and the AA radical form a direct stable bond. PLS is a radical of a polysaccharide; PLS-RU is a radical of a repeating unit of the polysaccharide; PAA is a radical of a polyamino acid, wherein the polyamino acid is selected from the group consisting of a homo-, a random and a block co-polyamino acid, with the proviso that the homo-polyamino acid is not polycationic; AA is a radical of an amino acid unit of the polyamino acid; subscript x of the radical is an integer ranging from 1 to 200; subscript v of the radical [ - x] is an integer ranging from 1 to 48; subscript w of the radical (PLS-RU) is an integer ranging from 1 to 200; In is a ROP initiator which comprises a terminal X group per each [ -] radical, wherein each terminal X group is directly bond to each [ -] radical, and wherein the terminal X group is selected form the group consisting of -NH-, -O-, -S-, or combinations thereof; CL is a radical selected from the group consisting of: (C 1 -C 500)-alkyl, wherein two or more H are substituted by: (C 1 -C 500)-alkyl; (C 3 -C 30)-cycloalkyl, C-radical derived from a ring system with 1-6 rings, each ring being independently saturated, partially unsaturated or aromatic, the rings of the ring system being isolated or fused and each ring having 3-20 elements each element independently selected from the group consisting of C, CH, CH 2, CO, O, S, N and NH, OH, NR a R b, ONR c R d, CN, halide, SH 2, SR e R f, N NH 2, R g COR h, COOR i, CON(R j)(R k), R l N(R m)CON(R n)(R' n), (C 1 -C 30)-alkene, (C 1 -C 30)-alkyne, N 3, R o CH(OR p)(OR q), R r CH(SR s)(SR t), R u B(OR v)(OR w), COR x; and wherein none, one of more C, are independently replaced by (C 3 -C 30)-cycloalkyl, aryl, aryl-(C 1 -C 30)-alkyl, NR y R z, CO, O, S, S, S(O 2), B, P and (O-CH 2 -CH 2) A; subscript A of the radical (O-CH 2 -CH 2) is an integer number between 1 and 500; R a, R b, R c, R d, R e, R f, R h, R i, R j, R k, R m, R n, R' n, R p, R q, R s, R t, R v, R w, R x, R y and R z are radicals independently selected from the group consisting of H, (C 1 -C 30)-alkyl, (C 1 -C 30)-alkylphenyl, phenyl-(C 1 -C 30)-alkyl, and (C 3 -C 8)-cycloalkyl; wherein, in any of them, except for H, one or more carbons are optionally substituted by a heteroatom selected from the group consisting of O, S, S, S(O 2), halide, N, NH, P, and CO; R g, R l, R o, R r and R u are radicals independently selected from the group consisting of (C 1 -C 30)-alkyl, (C 1 -C 30)-alkylphenyl, phenyl-(C 1 -C 30)-alkyl, and (C 3 -C 8)-cycloalkyl; wherein, one or more carbons are optionally substituted by a heteroatom selected from the group consisting of O, S, S, S(O 2), halide, N, NH, P, and CO; with the proviso that: CL may be present or not, so that if CL is not present, the PLS-RU radical and the AA radical form a direct stable bond.