A MEMS actuator (50; 280) comprising: - a body surrounding a cavity; - a deformable structure suspended on the cavity and comprising a movable portion and a plurality of deformable elements, arranged consecutively to each other, connecting the movable portion to the body and each subject to a deformation; and - at least one plurality of actuation structures (80A, 80B) supported by the deformable elements and configured to cause a translation of the movable portion greater than the deformation of each deformable element, the actuation structures each comprising a respective first piezoelectric region, wherein the first piezoelectric region is a thin-film piezoelectric layer, wherein: the deformable elements have a generally annular shape and surround the movable portion; the at least one plurality of actuation structures is a first plurality of actuation structures, the first plurality of actuation structures being configured to deform the deformable structure and move the movable portion along a first direction; the actuator further comprises a second plurality of actuation structures, the actuation structures of the second plurality of actuation structures each comprising a respective piezoelectric region equal to the first piezoelectric region, the second plurality of actuation structures being configured to deform the deformable structure and move the movable portion along a second direction, opposite to the first direction; and the actuation structures of the first and the second pluralities of actuation structures (80A, 80B) are arranged alternately in succession in each deformable element, wherein the deformable structure comprises a plurality of arms (60, 65, 70, 75); first arms of the plurality of arms extending between the body and the plurality of deformable elements; second arms (65, 70) of the plurality of arms extending between adjacent deformable elements of the plurality of deformable elements; and third arms of the plurality of arms extending between the plurality of deformable elements and the movable portion, wherein the second arms (65, 70) couple the actuation structures of the first plurality of actuation structures on the deformable elements to actuation structures of the second plurality of actuation structures on the adjacent deformable elements, and wherein the deformable structure further comprises a plurality of stiffening structures, the stiffening structures being supported by the deformable elements on an opposite side with respect to the actuation structures of the first plurality of actuation structures, each stiffening structure being arranged at a central portion of a respective actuation structure of the first plurality of actuation structures and being integral with a respective arm of the plurality of arms. - a body surrounding a cavity; - a deformable structure suspended on the cavity and comprising a movable portion and a plurality of deformable elements, arranged consecutively to each other, connecting the movable portion to the body and each subject to a deformation; and - at least one plurality of actuation structures (80A, 80B) supported by the deformable elements and configured to cause a translation of the movable portion greater than the deformation of each deformable element, the actuation structures each comprising a respective first piezoelectric region, wherein the first piezoelectric region is a thin-film piezoelectric layer, the deformable elements have a generally annular shape and surround the movable portion; the at least one plurality of actuation structures is a first plurality of actuation structures, the first plurality of actuation structures being configured to deform the deformable structure and move the movable portion along a first direction; the actuator further comprises a second plurality of actuation structures, the actuation structures of the second plurality of actuation structures each comprising a respective piezoelectric region equal to the first piezoelectric region, the second plurality of actuation structures being configured to deform the deformable structure and move the movable portion along a second direction, opposite to the first direction; and the actuation structures of the first and the second pluralities of actuation structures (80A, 80B) are arranged alternately in succession in each deformable element, wherein the deformable structure comprises a plurality of arms (60, 65, 70, 75); first arms of the plurality of arms extending between the body and the plurality of deformable elements; second arms (65, 70) of the plurality of arms extending between adjacent deformable elements of the plurality of deformable elements; and third arms of the plurality of arms extending between the plurality of deformable elements and the movable portion, wherein the second arms (65, 70) couple the actuation structures of the first plurality of actuation structures on the deformable elements to actuation structures of the second plurality of actuation structures on the adjacent deformable elements, and wherein the deformable structure further comprises a plurality of stiffening structures, the stiffening structures being supported by the deformable elements on an opposite side with respect to the actuation structures of the first plurality of actuation structures, each stiffening structure being arranged at a central portion of a respective actuation structure of the first plurality of actuation structures and being integral with a respective arm of the plurality of arms.