Voltage drops keeping the current same as source/supply curent
Try one of these switching regulators: -



This should just give you the general idea what you should be looking for although the part above is highly suited to your requirements and will work down to 2.7 volts from the Li ion battery. The resistor values shown can be any range within reason i.e. 140.9 kohm and 60.4 kohm. These are precise theoretical values so a 150 k and 62 k resistor would produce a nominal output of 2.05 volts.

You can of course use a linear regulator but it will be burning energy that you may want to conserve given it's a battery powered application. For instance, a linear regulator with 4.2 volts at the input and 2 volts at the output will be dissipating 4.4 watts of power (yuk) and probably need a fair sized heatsink. 

A switching regulator on the other hand will be 90%+ efficient so, if the output power is 4 watts (2 volts, 2 amps) then the input power will be 2.22 watts thus the switcher only burns 220 mW.

As with all these things read the data sheet.

Texas Instruments are another source and, if you are prepared to have an external transistor supplementing the switcher then there are many more options.