DescriptionLet l be a prime. For any algebraically closed field F of positive characteristic p different from l, we show that for all natural numbers n the nth stable homotopy group of spheres is isomorphic to the (n, 0) motivic stable homotopy group of spheres over F after inverting the characteristic of the field F. For a finite field F with q elements, we calculate the (n,0) motivic stable homotopy groups over F after inverting the characteristic of F for n < 19 with partial results when n = 19 and n = 20. This is achieved by studying the properties of the motivic Adams spectral sequence under base change and computer calculations of Ext groups.