The Simple Bluetooth Adapter is based on the KRC-86b, a cheap Bluetooth module found on eBay. It is a handy chip that handles the Bluetooth connection, the sound decoding and a first stage of amplification.
It is powered by a LiPo battery, a LT1302 boosts the output voltage from 3.7V to 5V. (This part is highly inspired by the MintyBoost schematics.)
Finally, a few more components were added to secure the charge and the discharge of the battery in addition of a load sharing circuit that allows to use the adapter while charging.
Notice: the schematic and files to manufacture the PCB are in the files section.