Texture not showing up on mesh

Hey,

I used the search function, but I did not find any answer to my specific problem. Most problems with materials and textures seem to occure when importing them from another program.

In my case its the following: I exported a fbx mesh from blender and imported it into unity. Now I want to assingn a material created in Unity to the mesh. It looks like the material is assigned properly, but the texture wont show up on it. It only appears in the colour the texture has. Im guessing it hast something to do with the UV Map, but I have no idea how to fix it. I created the UV Map in Blender, but I dont even know how it is imported via fbx... assigning the same material to a cube created in unity works fine...

I hope I described the problem in an understandable way and s.o. can help me.

Thanks in advance

David