Is it permissible for me to purchase goods not available in the store where I work and sell them to those who request them, splitting the profit with the store owner without his knowledge?

It is not permissible for a worker to sell anything for his own benefit at his workplace without the permission of the owner, whether the item sold belongs to the owner of the shop or to the worker. This is because he is a private employee, and his services are owned by the employer. He would be disposing of another's property without permission. However, if the owner of the shop grants him permission, then there is no harm, and the profit belongs solely to the worker. He is not obligated to give the shop owner half of the profit as rent, because the rent must be a known amount.