Check out my Modified Sine Wave Signal Generator. It might be just what you are looking for.
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To begin, I will assume that by inverter, you mean a circuit to convert DC to AC. If that is the case, I will also assume that the PIC (or any processor for that matter) would just be for generating the necessary drive to the power electronics (FETs, BJTs, etc) to prodce the output AC waveforms. The PIC aspect of a basic inverter is fairly straightforward. The design of working, safe, and reliable power electronics is much more of a challenge. If you don't need provide a large amount of output power, one easy way is to use an self contained H bridge module. These are often used for DC PM motor control, but they can be used for this application as well. These look like a large transistor, only they have many more leads. They take care of all the power electronic design concerns, you just have to supply a few support components along with power and ground and proper heatsinking. The control signals for modules like this often consist of just an on/off input and a direction input. The processor just generates the logic signal propely drive these signals to produce the output waveform. Generating the "modified sine wave " (google if you don't know what that is) type of output found in most cheaper off the shelf inverters can be accomplished with relatively simple code.
Why does it need to contain (or be based on??) a microcontroller? What do you want the microcontroller to do for/with/to it?
inverter without pic microcontroller THIS
Plenty out there, if you look. What do you want to do ? What have you already tried ?