General:
* Create
* Construct
* Make
* Manufacture
* Invent
* Forge
* Devise
With a negative connotation (to lie or make something up):
* Concoct
* Cook up
* Make up
* Compose
* Fashion
* Feign
More specific:
* Assemble (to put together parts)
* Assemble (to gather and organize information)
* Manufacture (to produce something on a large scale)
* Forge (to create something illegally or dishonestly)
* Counterfeit (to make an imitation of something)
* Emulate (to copy something)
The best synonym will depend on the specific context and the nuance you want to convey.