"Can a colony eventually refund it's investors that helped fund it's deployment through some sort of value generated on their home planet and 'transported' to earth through ansible communication."

Very unlikely. The inability to exchange tangible resources means that the colony cannot export its surplus production. Given that the colony is likely to be resource rich but information and culture poor, the investment outlook is not good. Unless you come up with a plotline to superpower the colony information economy they will be a net surplus natural resource producer and an importer of services and information.

The surplus goods in the colony will lead to deflation in those sectors, their currency will depreciate against the homeworld and the price of imported information and services will rocket.

Ultimately any currency has to convey to the holder the right to consume, and consumption is synonymous with the dissipation of free energy (by eating food, driving vehicles, using google search etc). It is not obvious why long term terrestrial investors would invest in the colony since any claims on the conoly cannot be used for consumption on earth.

A purely service/culture based exchange would likely end up driving bubbles and speculation before a final deflationary collapse. In reality economies need to be grounded in the real economy of physical consumption.

"Can a colony eventually refund it's investors that helped fund it's deployment through some sort of value generated on their home planet and 'transported' to earth through ansible communication."

Very unlikely. The inability to exchange tangible resources means that the colony cannot export its surplus production. Given that the colony is likely to be resource rich but information and culture poor, the investment outlook is not good. Unless you come up with a plotline to superpower the colony information economy (like they can produce some super-comptronium and be the data centre for the earth) they will be a net surplus natural resource producer and an importer of services and information.

The surplus goods in the colony will lead to deflation in those sectors, their currency will depreciate against the homeworld and the price of imported information and services will rocket.

Ultimately any currency has to convey to the holder the right to consume, and consumption is synonymous with the dissipation of free energy (by eating food, driving vehicles, using google search etc). It is not obvious why long term terrestrial investors would invest in the colony since any claims on the colony cannot be used for consumption on earth.

A purely service/culture based exchange would likely end up driving bubbles and speculation before a final deflationary collapse. In reality economies need to be grounded in the real economy of physical consumption.