Active, programmable control of interfacial adhesion is an important, desired feature of many existing and envisioned systems, including medical tapes, releasable joints, and stamps for transfer printing. Here a design for an elastomeric surface that offers switchable adhesion strength through a combination of peel-rate dependent effects and actuation of sub-surface fluid chambers is presented. Microchannels and open reservoirs positioned under a thin surface membrane can be pressurized in a controlled manner to induce various levels of surface deformation via inflation. These pressurized structures demonstrate utility in controllably decreasing the strength of adhesion of flat, solid objects to the elastomeric surface, particularly in the limit of low peel-rates. Experimental and theoretical studies of these systems reveal the key mechanisms, and guide optimized geometries for broad control over adhesion, in a programmable and reversible manner. Implementing these concepts in stamps for transfer printing enables new modes for deterministic assembly of micro- and nanoscale materials onto diverse types of substrates. Collections of silicon plates delivered onto plastic, paper and other surfaces with single or multiply addressable stamps illustrate some of the capabilities.