Formal orbifolds and orbifold bundles in positive characteristic

We define formal orbifolds over an algebraically closed field of arbitrary characteristic as curves together with some branch data. Their \'etale coverings and their fundamental groups are also defined. These fundamental group approximates the fundamental group of an appropriate affine curve. We also define vector bundles on these objects and the category of orbifold bundles on any smooth projective curve. Analogues of various statement about vector bundles which are true in characteristic zero are proved. Some of these are positive characteristic avatar of notions which appear in the second author's work ([Par]) in characteristic zero.