Convert DC 1.5V to 2.7V
You need a DC-DC Boost Converter. You won't be able to get more power than the cell can provide&mdash;in fact, you'll get less due to efficiency losses in the boost converter. Since you're boosting the voltage, you have to settle for less amperage.

$$P = IE$$

So if your R20 1.5V cell can sustain 2A, that provides for a load of 1.5 * 2 = 3W.

If you use a boost converter with 90% efficiency, you would get 2.7W out of it. Calculating for 2.6V (I = W/E) shows that the current would then be ~1.04A.